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Model Deployment : Detecting and Analyzing Machine Learning Model Drift Using Open-Source Monitoring Tools

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John Pauline Pineda

October 31, 2025

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• 1. Table of Contents
  • 1.1 Data Background
  • 1.2 Data Description
  • 1.3 Data Quality Assessment
  • 1.4 Data Preprocessing
    • 1.4.1 Data Splitting
    • 1.4.2 Outlier and Distributional Shape Analysis
    • 1.4.3 Collinearity
  • 1.5 Data Exploration
    • 1.5.1 Exploratory Data Analysis
    • 1.5.2 Hypothesis Testing
  • 1.6 Premodelling Data Preparation
    • 1.6.1 Preprocessed Data Description
    • 1.6.2 Preprocessing Pipeline Development
  • 1.7 Model Development and Validation
    • 1.7.1 Random Forest
    • 1.7.2 AdaBoost
    • 1.7.3 Gradient Boosting
    • 1.7.4 XGBoost
    • 1.7.5 Light GBM
    • 1.7.6 CatBoost
  • 1.8 Model Selection
  • 1.9 Model Monitoring using the NannyML Framework
    • 1.9.1 Simulated Baseline Control
    • 1.9.2 Simulated Covariate Drift
    • 1.9.3 Simulated Prior Shift
    • 1.9.4 Simulated Concept Drift
    • 1.9.5 Simulated Missingness Spike
    • 1.9.6 Simulated Seasonal Pattern
  • 1.10 Consolidated Findings
• 2. Summary
• 3. References

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1. Table of Contents

This project investigates open-source frameworks for post-deployment model monitoring and performance estimation, with a particular focus on NannyML or detecting and interpreting shifts in machine learning pipelines using Python. The objective was to systematically analyze how different types of drift and distribution changes manifest after model deployment, and to demonstrate how robust monitoring mitigates risks of performance degradation and biased decision-making. The workflow began with the development and selection of a baseline predictive model, which serves as a reference for stability. The dataset was then deliberately perturbed to simulate a range of realistic post-deployment scenarios: Covariate Drift (shifts in feature distributions), Prior Shift (changes in target label proportions), Concept Drift (evolving relationships between features and outcomes), Missingness Spikes (abrupt increases in absent data), and Seasonal Patterns (periodic variations in distributions). NannyML’s statistical tests, visualization capabilities, and performance estimation methods were subsequently applied to diagnose these shifts, evaluate their potential impact, and provide interpretable insights into model reliability. By contrasting baseline and perturbed conditions, the experiment demonstrated how continuous monitoring augments traditional offline evaluation, offering a safeguard against hidden risks. The findings highlighted how tools like NannyML can integrate seamlessly into MLOps workflows to enable proactive governance, early warning systems, and sustainable deployment practices. All results were consolidated in a Summary presented at the end of the document.

Post-Deployment Monitoring refers to the continuous oversight of machine learning models once they are integrated into production systems. Unlike offline evaluation, which relies on static validation datasets, monitoring addresses the challenges of evolving real-world data streams where underlying distributions may shift. Effective monitoring ensures that models remain accurate, unbiased, and aligned with business objectives. In MLOps, monitoring encompasses data integrity checks, drift detection, performance estimation, and alerting mechanisms. NannyML operationalizes this concept by focusing on performance estimation without ground truth, and by offering statistical methods to detect when data or predictions deviate from expected baselines. The challenges of post-deployment monitoring include delayed or missing ground truth labels, non-stationary data, hidden feedback loops, and difficulties distinguishing natural fluctuations from problematic drifts. Common solutions involve deploying drift detection algorithms, conducting regular audits of data pipelines, simulating counterfactuals, and retraining models on updated data. Monitoring frameworks must balance sensitivity (detecting real problems quickly) with robustness (avoiding false alarms caused by natural noise). Another key challenge is explainability: stakeholders need interpretable signals that justify interventions such as retraining or rolling back models. Tools like NannyML address these challenges through statistical tests for data drift, performance estimation without labels, missingness tracking, and visual diagnostics, making monitoring actionable for data scientists and business teams alike.

Covariate Drift occurs when the distribution of input features changes over time compared to the data used to train the model. Also known as data drift, it does not necessarily imply that the model’s predictive mapping is invalid, but it often precedes performance degradation. Detecting covariate drift requires comparing feature distributions between baseline (reference) data and incoming production data. NannyML provides multiple statistical tests and visualization tools to flag significant changes. Key signatures of covariate drift include shifts in summary statistics (mean, variance), changes in distributional shape, or increased divergence between reference and production feature distributions. These shifts may lead to poor generalization, as the model has not been exposed to the altered feature ranges. Detection techniques include univariate statistical tests (e.g., Kolmogorov–Smirnov, Chi-square), multivariate distance measures (e.g., Jensen–Shannon divergence, Population Stability Index), and density estimation methods. Remediation approaches involve domain adaptation, re-weighting training samples, or retraining models on updated data distributions. NannyML implements univariate and multivariate tests, provides drift magnitude quantification, and visualizes feature-level changes, allowing practitioners to pinpoint which features are most responsible for the detected drift.

Prior Shift arises when the distribution of the target variable changes, while the conditional relationship between features and labels remains stable. This is also referred to as label shift. Models trained on the original distribution may underperform because their predictions no longer match the new class priors. Detecting prior shifts is crucial, especially in imbalanced classification tasks where small changes in priors can lead to large performance impacts. Prior shift is typically characterized by systematic increases or decreases in class frequencies without corresponding changes in feature distributions. Its impact includes skewed decision thresholds, inflated false positives/negatives, and degraded calibration of predicted probabilities. Detection approaches include monitoring predicted class proportions, estimating priors using EM-based algorithms, and re-weighting predictions to align with new distributions. Correction strategies may involve resampling, threshold adjustment, or cost-sensitive learning. NannyML assists by tracking predicted probability distributions and comparing them against reference priors, using techniques such as KL divergence and PSI to quantify the magnitude of shift.

Concept Drift occurs when the underlying relationship between input features and target labels evolves over time. Unlike covariate drift, where features change independently, concept drift implies that the model’s mapping function itself becomes outdated. Concept drift is among the most damaging forms of drift because it directly undermines predictive accuracy. Detecting it often requires monitoring model outputs or inferred performance over time. NannyML addresses this by estimating performance even when ground truth labels are unavailable. Concept drift is typically signaled by a gradual or sudden decline in performance metrics, inconsistent error patterns, or misalignment between expected and actual prediction behavior. Its impact is severe: models may lose predictive power entirely if they cannot adapt. Detection methods include window-based performance monitoring, hypothesis testing, adaptive ensembles, and statistical monitoring of residuals. Corrective actions include periodic retraining, incremental learning, and online adaptation strategies. NannyML leverages Confidence-Based Performance Estimation (CBPE) and other statistical techniques to estimate performance degradation without labels, making it possible to detect concept drift in real-time production environments.

Missingness Spike refers to sudden increases in missing values within production data. Missing features can destabilize preprocessing pipelines, distort predictions, and signal upstream data collection failures. Monitoring missingness is critical for ensuring both model reliability and data pipeline health. NannyML provides built-in mechanisms to track and visualize changes in missing data patterns, alerting stakeholders before downstream impacts occur. Key indicators of missingness spikes include abrupt rises in null counts, missing categorical levels, or structural breaks in feature completeness. The consequences range from biased predictions to outright system failures if preprocessing pipelines cannot handle unexpected missingness. Detection methods include statistical monitoring of missing value proportions, anomaly detection on completeness metrics, and threshold-based alerts. Solutions typically involve robust imputation, pipeline hardening, and upstream data validation. NannyML offers automated missingness detection, completeness trend visualization, and configurable thresholds, ensuring that missingness issues are surfaced early.

Seasonal Pattern Shift represents periodic fluctuations in data distributions or outcomes that follow predictable cycles. If models are not trained with sufficient historical data to capture these patterns, their predictions may systematically underperform during certain periods. NannyML’s monitoring can reveal recurring deviations, helping teams distinguish between natural seasonality and genuine drift that requires retraining. Seasonality is often characterized by cyclic patterns in data features, prediction distributions, or performance metrics. Its impact includes systematic biases, recurring error peaks, and difficulty distinguishing drift from natural variability. Detection techniques include autocorrelation analysis, Fourier decomposition, and seasonal-trend decomposition. Mitigation strategies involve training with longer historical datasets, adding time-related features, or developing seasonally adaptive models. NannyML highlights recurring deviations in drift metrics, making it easier for practitioners to separate cyclical behavior from true degradation, ensuring that alerts are contextually relevant.

Performance Estimation Without Labels refers to scenarios in real-world deployments where the ground truth often arrives with delays—or may never be available. This makes direct performance tracking difficult. NannyML addresses this challenge by providing algorithms to estimate model performance without labels using confidence distributions, statistical inference, and robust estimation techniques. This capability allows practitioners to maintain visibility into model health continuously, even in label-scarce settings, bridging a critical gap in MLOps monitoring practices. Algorithms in this domain include Confidence-Based Performance Estimation (CBPE), which infers performance by comparing predicted probability distributions against expected confidence intervals, and Direct Loss Estimation, which approximates error rates based on calibration. Statistical inference techniques allow practitioners to construct confidence bounds around estimated metrics, while robust estimation mitigates the risk of spurious signals caused by small sample sizes or noisy predictions. NannyML provides implementations of CBPE and DLE, supporting metrics such as precision, recall, F1-score, and AUROC, all estimated without labels. This makes it possible to detect when a model is underperforming even before labels are collected, reducing blind spots in production monitoring.

Performance Estimation With Labels refers to the direct evaluation of model predictions against actual ground truth outcomes once labels are available. Unlike label-free methods, this approach allows for precise calculation of traditional performance metrics such as accuracy, precision, recall, F1-score, AUROC, and calibration error. Monitoring with labels provides the most reliable indication of model performance, enabling fine-grained diagnosis of errors and biases. The advantage of having labels is the ability to attribute errors to specific subgroups, detect fairness violations, and conduct targeted retraining. Challenges include label delay, annotation quality, and ensuring that labels accurately reflect the operational environment. Common approaches include sliding window evaluation, where performance is tracked over recent data batches, and benchmark comparison, where production metrics are compared to baseline test set results. NannyML incorporates labeled performance tracking alongside its label-free estimators, allowing users to validate estimates once ground truth becomes available. This dual capability ensures consistency, improves confidence in label-free methods, and provides a comprehensive framework for performance monitoring in both short-term and long-term horizons.

1.1. Data Background

An open Breast Cancer Dataset from Kaggle (with all credits attributed to Wasiq Ali) was used for the analysis as consolidated from the following primary sources:

1. Reference Repository entitled Differentiated breast Cancer Recurrence from UC Irvine Machine Learning Repository
2. Research Paper entitled Nuclear Feature Extraction for Breast Tumor Diagnosis from the Electronic Imaging

This study hypothesized that the cell nuclei features derived from digitized images of fine needle aspirates (FNA) of breast masses influence breast cancer diagnoses between patients.

The dichotomous categorical variable for the study is:

• diagnosis - Status of the patient (M, Medical diagnosis of a cancerous breast tumor | B, Medical diagnosis of a non-cancerous breast tumor)

The predictor variables for the study are:

• radius_mean - Mean of the radius measurements (Mean of distances from center to points on the perimeter)
• texture_mean - Mean of the texture measurements (Standard deviation of grayscale values)
• perimeter_mean - Mean of the perimeter measurements
• area_mean - Mean of the area measurements
• smoothness_mean - Mean of the smoothness measurements (Local variation in radius lengths)
• compactness_mean - Mean of the compactness measurements (Perimeter² / area - 1.0)
• concavity_mean - Mean of the concavity measurements (Severity of concave portions of the contour)
• concave points_mean - Mean of the concave points measurements (Number of concave portions of the contour)
• symmetry_mean - Mean of the symmetry measurements
• fractal_dimension_mean - Mean of the fractal dimension measurements (Coastline approximation - 1)
• radius_se - Standard error of the radius measurements (Standard error of distances from center to points on the perimeter)
• texture_se - Standard error of the texture measurements (Standard deviation of grayscale values)
• perimeter_se - Standard error of the perimeter measurements
• area_se - Standard error of the area measurements
• smoothness_se - Standard error of the smoothness measurements (Local variation in radius lengths)
• compactness_se - Standard error of the compactness measurements (Perimeter² / area - 1.0)
• concavity_se - Standard error of the concavity measurements (Severity of concave portions of the contour)
• concave points_se - Standard error of the concave points measurements (Number of concave portions of the contour)
• symmetry_se - Standard error of the symmetry measurements
• fractal_dimension_se - Standard error of the fractal dimension measurements (Coastline approximation - 1)
• radius_worst - Largest value of the radius measurements (Largest value of distances from center to points on the perimeter)
• texture_worst - Largest value of the texture measurements (Standard deviation of grayscale values)
• perimeter_worst - Largest value of the perimeter measurements
• area_worst - Largest value of the area measurements
• smoothness_worst - Largest value of the smoothness measurements (Local variation in radius lengths)
• compactness_worst - Largest value of the compactness measurements (Perimeter² / area - 1.0)
• concavity_worst - Largest value of the concavity measurements (Severity of concave portions of the contour)
• concave points_worst - Largest value of the concave points measurements (Number of concave portions of the contour)
• symmetry_worst - Largest value of the symmetry measurements
• fractal_dimension_worst - Largest value of the fractal dimension measurements (Coastline approximation - 1)

1.2. Data Description

1. The initial tabular dataset was comprised of 569 observations and 32 variables (including 1 metadata, 1 target and 30 predictors).
   • 569 rows (observations)
   • 32 columns (variables)
     • 1/32 metadata (categorical)
       • id
     • 1/32 target (categorical)
       • diagnosis
     • 30/32 predictor (numeric)
       • radius_mean
       • texture_mean
       • perimeter_mean
       • area_mean
       • smoothness_mean
       • compactness_mean
       • concavity_mean
       • concave points_mean
       • symmetry_mean
       • fractal_dimension_mean
       • radius_se
       • texture_se
       • perimeter_se
       • area_se
       • smoothness_se
       • compactness_se
       • concavity_se
       • concave points_se
       • symmetry_se
       • fractal_dimension_se
       • radius_worst
       • texture_worst
       • perimeter_worst
       • area_worst
       • smoothness_worst
       • compactness_worst
       • concavity_worst
       • concave points_worst
       • symmetry_worst
       • fractal_dimension_worst
2. The id variable was transformed to a row index for the data observations.

##################################
# Loading Python Libraries
##################################
import numpy as np
import pandas as pd
import seaborn as sns
import matplotlib.pyplot as plt
import os
import joblib
import re
import pickle
%matplotlib inline

import nannyml as nml
from nannyml.performance_estimation import CBPE
from nannyml.chunk import DefaultChunker

import hashlib
import json
from urllib.parse import urlparse
import logging

from operator import truediv
from sklearn.preprocessing import StandardScaler, FunctionTransformer
from sklearn.decomposition import PCA
from scipy import stats
from scipy.stats import pointbiserialr, chi2_contingency

from sklearn.pipeline import Pipeline
from sklearn.compose import ColumnTransformer
from sklearn.tree import DecisionTreeClassifier
from sklearn.ensemble import RandomForestClassifier, AdaBoostClassifier, GradientBoostingClassifier
from sklearn.impute import SimpleImputer
from xgboost import XGBClassifier
from lightgbm import LGBMClassifier
from catboost import CatBoostClassifier
from sklearn.metrics import accuracy_score, precision_score, recall_score, f1_score, roc_auc_score, confusion_matrix, classification_report
from sklearn.model_selection import train_test_split, ParameterGrid, StratifiedShuffleSplit, RepeatedStratifiedKFold, GridSearchCV
from sklearn.utils import resample
from sklearn.base import clone

import warnings
warnings.filterwarnings("ignore", message=".*force_all_finite.*")
warnings.filterwarnings("ignore", message="X does not have valid feature names")

##################################
# Defining file paths
##################################
DATASETS_ORIGINAL_PATH = r"datasets\original"
DATASETS_FINAL_PATH = r"datasets\final\complete"
DATASETS_FINAL_TRAIN_PATH = r"datasets\final\train"
DATASETS_FINAL_TRAIN_FEATURES_PATH = r"datasets\final\train\features"
DATASETS_FINAL_TRAIN_TARGET_PATH = r"datasets\final\train\target"
DATASETS_FINAL_VALIDATION_PATH = r"datasets\final\validation"
DATASETS_FINAL_VALIDATION_FEATURES_PATH = r"datasets\final\validation\features"
DATASETS_FINAL_VALIDATION_TARGET_PATH = r"datasets\final\validation\target"
DATASETS_FINAL_TEST_PATH = r"datasets\final\test"
DATASETS_FINAL_TEST_FEATURES_PATH = r"datasets\final\test\features"
DATASETS_FINAL_TEST_TARGET_PATH = r"datasets\final\test\target"
DATASETS_PREPROCESSED_PATH = r"datasets\preprocessed"
DATASETS_PREPROCESSED_TRAIN_PATH = r"datasets\preprocessed\train"
DATASETS_PREPROCESSED_TRAIN_FEATURES_PATH = r"datasets\preprocessed\train\features"
DATASETS_PREPROCESSED_TRAIN_TARGET_PATH = r"datasets\preprocessed\train\target"
DATASETS_PREPROCESSED_VALIDATION_PATH = r"datasets\preprocessed\validation"
DATASETS_PREPROCESSED_VALIDATION_FEATURES_PATH = r"datasets\preprocessed\validation\features"
DATASETS_PREPROCESSED_VALIDATION_TARGET_PATH = r"datasets\preprocessed\validation\target"
DATASETS_PREPROCESSED_TEST_PATH = r"datasets\preprocessed\test"
DATASETS_PREPROCESSED_TEST_FEATURES_PATH = r"datasets\preprocessed\test\features"
DATASETS_PREPROCESSED_TEST_TARGET_PATH = r"datasets\preprocessed\test\target"
MODELS_PATH = r"models"

##################################
# Loading the dataset
# from the DATASETS_ORIGINAL_PATH
##################################
breast_cancer = pd.read_csv(os.path.join("..", DATASETS_ORIGINAL_PATH, "Breast_Cancer_Dataset.csv"))

##################################
# Performing a general exploration of the dataset
##################################
print('Dataset Dimensions: ')
display(breast_cancer.shape)

Dataset Dimensions: 

(569, 32)

##################################
# Listing the column names and data types
##################################
print('Column Names and Data Types:')
display(breast_cancer.dtypes)

Column Names and Data Types:

id                           int64
diagnosis                   object
radius_mean                float64
texture_mean               float64
perimeter_mean             float64
area_mean                  float64
smoothness_mean            float64
compactness_mean           float64
concavity_mean             float64
concave points_mean        float64
symmetry_mean              float64
fractal_dimension_mean     float64
radius_se                  float64
texture_se                 float64
perimeter_se               float64
area_se                    float64
smoothness_se              float64
compactness_se             float64
concavity_se               float64
concave points_se          float64
symmetry_se                float64
fractal_dimension_se       float64
radius_worst               float64
texture_worst              float64
perimeter_worst            float64
area_worst                 float64
smoothness_worst           float64
compactness_worst          float64
concavity_worst            float64
concave points_worst       float64
symmetry_worst             float64
fractal_dimension_worst    float64
dtype: object

##################################
# Setting the ID column as row names
##################################
breast_cancer = breast_cancer.set_index("id")

##################################
# Taking a snapshot of the dataset
##################################
breast_cancer.head()

	diagnosis	radius_mean	texture_mean	perimeter_mean	area_mean	smoothness_mean	compactness_mean	concavity_mean	concave points_mean	symmetry_mean	...	radius_worst	texture_worst	perimeter_worst	area_worst	smoothness_worst	compactness_worst	concavity_worst	concave points_worst	symmetry_worst	fractal_dimension_worst
id
842302	M	17.99	10.38	122.80	1001.0	0.11840	0.27760	0.3001	0.14710	0.2419	...	25.38	17.33	184.60	2019.0	0.1622	0.6656	0.7119	0.2654	0.4601	0.11890
842517	M	20.57	17.77	132.90	1326.0	0.08474	0.07864	0.0869	0.07017	0.1812	...	24.99	23.41	158.80	1956.0	0.1238	0.1866	0.2416	0.1860	0.2750	0.08902
84300903	M	19.69	21.25	130.00	1203.0	0.10960	0.15990	0.1974	0.12790	0.2069	...	23.57	25.53	152.50	1709.0	0.1444	0.4245	0.4504	0.2430	0.3613	0.08758
84348301	M	11.42	20.38	77.58	386.1	0.14250	0.28390	0.2414	0.10520	0.2597	...	14.91	26.50	98.87	567.7	0.2098	0.8663	0.6869	0.2575	0.6638	0.17300
84358402	M	20.29	14.34	135.10	1297.0	0.10030	0.13280	0.1980	0.10430	0.1809	...	22.54	16.67	152.20	1575.0	0.1374	0.2050	0.4000	0.1625	0.2364	0.07678

5 rows × 31 columns

##################################
# Performing a general exploration of the numeric variables
##################################
print('Numeric Variable Summary:')
display(breast_cancer.describe(include='number').transpose())

Numeric Variable Summary:

	count	mean	std	min	25%	50%	75%	max
radius_mean	569.0	14.127292	3.524049	6.981000	11.700000	13.370000	15.780000	28.11000
texture_mean	569.0	19.289649	4.301036	9.710000	16.170000	18.840000	21.800000	39.28000
perimeter_mean	569.0	91.969033	24.298981	43.790000	75.170000	86.240000	104.100000	188.50000
area_mean	569.0	654.889104	351.914129	143.500000	420.300000	551.100000	782.700000	2501.00000
smoothness_mean	569.0	0.096360	0.014064	0.052630	0.086370	0.095870	0.105300	0.16340
compactness_mean	569.0	0.104341	0.052813	0.019380	0.064920	0.092630	0.130400	0.34540
concavity_mean	569.0	0.088799	0.079720	0.000000	0.029560	0.061540	0.130700	0.42680
concave points_mean	569.0	0.048919	0.038803	0.000000	0.020310	0.033500	0.074000	0.20120
symmetry_mean	569.0	0.181162	0.027414	0.106000	0.161900	0.179200	0.195700	0.30400
fractal_dimension_mean	569.0	0.062798	0.007060	0.049960	0.057700	0.061540	0.066120	0.09744
radius_se	569.0	0.405172	0.277313	0.111500	0.232400	0.324200	0.478900	2.87300
texture_se	569.0	1.216853	0.551648	0.360200	0.833900	1.108000	1.474000	4.88500
perimeter_se	569.0	2.866059	2.021855	0.757000	1.606000	2.287000	3.357000	21.98000
area_se	569.0	40.337079	45.491006	6.802000	17.850000	24.530000	45.190000	542.20000
smoothness_se	569.0	0.007041	0.003003	0.001713	0.005169	0.006380	0.008146	0.03113
compactness_se	569.0	0.025478	0.017908	0.002252	0.013080	0.020450	0.032450	0.13540
concavity_se	569.0	0.031894	0.030186	0.000000	0.015090	0.025890	0.042050	0.39600
concave points_se	569.0	0.011796	0.006170	0.000000	0.007638	0.010930	0.014710	0.05279
symmetry_se	569.0	0.020542	0.008266	0.007882	0.015160	0.018730	0.023480	0.07895
fractal_dimension_se	569.0	0.003795	0.002646	0.000895	0.002248	0.003187	0.004558	0.02984
radius_worst	569.0	16.269190	4.833242	7.930000	13.010000	14.970000	18.790000	36.04000
texture_worst	569.0	25.677223	6.146258	12.020000	21.080000	25.410000	29.720000	49.54000
perimeter_worst	569.0	107.261213	33.602542	50.410000	84.110000	97.660000	125.400000	251.20000
area_worst	569.0	880.583128	569.356993	185.200000	515.300000	686.500000	1084.000000	4254.00000
smoothness_worst	569.0	0.132369	0.022832	0.071170	0.116600	0.131300	0.146000	0.22260
compactness_worst	569.0	0.254265	0.157336	0.027290	0.147200	0.211900	0.339100	1.05800
concavity_worst	569.0	0.272188	0.208624	0.000000	0.114500	0.226700	0.382900	1.25200
concave points_worst	569.0	0.114606	0.065732	0.000000	0.064930	0.099930	0.161400	0.29100
symmetry_worst	569.0	0.290076	0.061867	0.156500	0.250400	0.282200	0.317900	0.66380
fractal_dimension_worst	569.0	0.083946	0.018061	0.055040	0.071460	0.080040	0.092080	0.20750

1.3. Data Quality Assessment

Data quality findings based on assessment are as follows:

1. No duplicated rows were noted.
2. No missing data noted for any variable with Null.Count>0 and Fill.Rate<1.0.
3. No low variance observed for any variable with First.Second.Mode.Ratio>5.
4. No low variance observed for any variable with Unique.Count.Ratio>10.
5. High skewness observed for 5 variables with Skewness>3 or Skewness<(-3).
   • area_se: Skewness = 5.447
   • concavity_se: Skewness = 5.110
   • fractal_dimension_se: Skewness = 3.923
   • perimeter_se: Skewness = 3.443
   • radius_se: Skewness = 3.088

##################################
# Counting the number of duplicated rows
##################################
breast_cancer.duplicated().sum()

np.int64(0)

##################################
# Gathering the data types for each column
##################################
data_type_list = list(breast_cancer.dtypes)

##################################
# Gathering the variable names for each column
##################################
variable_name_list = list(breast_cancer.columns)

##################################
# Gathering the number of observations for each column
##################################
row_count_list = list([len(breast_cancer)] * len(breast_cancer.columns))

##################################
# Gathering the number of missing data for each column
##################################
null_count_list = list(breast_cancer.isna().sum(axis=0))

##################################
# Gathering the number of non-missing data for each column
##################################
non_null_count_list = list(breast_cancer.count())

##################################
# Gathering the missing data percentage for each column
##################################
fill_rate_list = map(truediv, non_null_count_list, row_count_list)

##################################
# Formulating the summary
# for all columns
##################################
all_column_quality_summary = pd.DataFrame(zip(variable_name_list,
                                              data_type_list,
                                              row_count_list,
                                              non_null_count_list,
                                              null_count_list,
                                              fill_rate_list), 
                                        columns=['Column.Name',
                                                 'Column.Type',
                                                 'Row.Count',
                                                 'Non.Null.Count',
                                                 'Null.Count',                                                 
                                                 'Fill.Rate'])
display(all_column_quality_summary)

	Column.Name	Column.Type	Row.Count	Non.Null.Count	Null.Count	Fill.Rate
0	diagnosis	object	569	569	0	1.0
1	radius_mean	float64	569	569	0	1.0
2	texture_mean	float64	569	569	0	1.0
3	perimeter_mean	float64	569	569	0	1.0
4	area_mean	float64	569	569	0	1.0
5	smoothness_mean	float64	569	569	0	1.0
6	compactness_mean	float64	569	569	0	1.0
7	concavity_mean	float64	569	569	0	1.0
8	concave points_mean	float64	569	569	0	1.0
9	symmetry_mean	float64	569	569	0	1.0
10	fractal_dimension_mean	float64	569	569	0	1.0
11	radius_se	float64	569	569	0	1.0
12	texture_se	float64	569	569	0	1.0
13	perimeter_se	float64	569	569	0	1.0
14	area_se	float64	569	569	0	1.0
15	smoothness_se	float64	569	569	0	1.0
16	compactness_se	float64	569	569	0	1.0
17	concavity_se	float64	569	569	0	1.0
18	concave points_se	float64	569	569	0	1.0
19	symmetry_se	float64	569	569	0	1.0
20	fractal_dimension_se	float64	569	569	0	1.0
21	radius_worst	float64	569	569	0	1.0
22	texture_worst	float64	569	569	0	1.0
23	perimeter_worst	float64	569	569	0	1.0
24	area_worst	float64	569	569	0	1.0
25	smoothness_worst	float64	569	569	0	1.0
26	compactness_worst	float64	569	569	0	1.0
27	concavity_worst	float64	569	569	0	1.0
28	concave points_worst	float64	569	569	0	1.0
29	symmetry_worst	float64	569	569	0	1.0
30	fractal_dimension_worst	float64	569	569	0	1.0

##################################
# Counting the number of columns
# with Fill.Rate < 1.00
##################################
len(all_column_quality_summary[(all_column_quality_summary['Fill.Rate']<1)])

0

##################################
# Identifying the rows
# with Fill.Rate < 0.90
##################################
column_low_fill_rate = all_column_quality_summary[(all_column_quality_summary['Fill.Rate']<0.90)]

##################################
# Gathering the indices for each observation
##################################
row_index_list = breast_cancer.index

##################################
# Gathering the number of columns for each observation
##################################
column_count_list = list([len(breast_cancer.columns)] * len(breast_cancer))

##################################
# Gathering the number of missing data for each row
##################################
null_row_list = list(breast_cancer.isna().sum(axis=1))

##################################
# Gathering the missing data percentage for each column
##################################
missing_rate_list = map(truediv, null_row_list, column_count_list)

##################################
# Identifying the rows
# with missing data
##################################
all_row_quality_summary = pd.DataFrame(zip(row_index_list,
                                           column_count_list,
                                           null_row_list,
                                           missing_rate_list), 
                                        columns=['Row.Name',
                                                 'Column.Count',
                                                 'Null.Count',                                                 
                                                 'Missing.Rate'])
display(all_row_quality_summary)

	Row.Name	Column.Count	Null.Count	Missing.Rate
0	842302	31	0	0.0
1	842517	31	0	0.0
2	84300903	31	0	0.0
3	84348301	31	0	0.0
4	84358402	31	0	0.0
...	...	...	...	...
564	926424	31	0	0.0
565	926682	31	0	0.0
566	926954	31	0	0.0
567	927241	31	0	0.0
568	92751	31	0	0.0

569 rows × 4 columns

##################################
# Counting the number of rows
# with Missing.Rate > 0.00
##################################
len(all_row_quality_summary[(all_row_quality_summary['Missing.Rate']>0.00)])

0

##################################
# Formulating the dataset
# with numeric columns only
##################################
breast_cancer_numeric = breast_cancer.select_dtypes(include='number')

##################################
# Gathering the variable names for each numeric column
##################################
numeric_variable_name_list = breast_cancer_numeric.columns

##################################
# Gathering the minimum value for each numeric column
##################################
numeric_minimum_list = breast_cancer_numeric.min()

##################################
# Gathering the mean value for each numeric column
##################################
numeric_mean_list = breast_cancer_numeric.mean()

##################################
# Gathering the median value for each numeric column
##################################
numeric_median_list = breast_cancer_numeric.median()

##################################
# Gathering the maximum value for each numeric column
##################################
numeric_maximum_list = breast_cancer_numeric.max()

##################################
# Gathering the first mode values for each numeric column
##################################
numeric_first_mode_list = [breast_cancer[x].value_counts(dropna=True).index.tolist()[0] for x in breast_cancer_numeric]

##################################
# Gathering the second mode values for each numeric column
##################################
numeric_second_mode_list = [breast_cancer[x].value_counts(dropna=True).index.tolist()[1] for x in breast_cancer_numeric]

##################################
# Gathering the count of first mode values for each numeric column
##################################
numeric_first_mode_count_list = [breast_cancer_numeric[x].isin([breast_cancer[x].value_counts(dropna=True).index.tolist()[0]]).sum() for x in breast_cancer_numeric]

##################################
# Gathering the count of second mode values for each numeric column
##################################
numeric_second_mode_count_list = [breast_cancer_numeric[x].isin([breast_cancer[x].value_counts(dropna=True).index.tolist()[1]]).sum() for x in breast_cancer_numeric]

##################################
# Gathering the first mode to second mode ratio for each numeric column
##################################
numeric_first_second_mode_ratio_list = map(truediv, numeric_first_mode_count_list, numeric_second_mode_count_list)

##################################
# Gathering the count of unique values for each numeric column
##################################
numeric_unique_count_list = breast_cancer_numeric.nunique(dropna=True)

##################################
# Gathering the number of observations for each numeric column
##################################
numeric_row_count_list = list([len(breast_cancer_numeric)] * len(breast_cancer_numeric.columns))

##################################
# Gathering the unique to count ratio for each numeric column
##################################
numeric_unique_count_ratio_list = map(truediv, numeric_unique_count_list, numeric_row_count_list)

##################################
# Gathering the skewness value for each numeric column
##################################
numeric_skewness_list = breast_cancer_numeric.skew()

##################################
# Gathering the kurtosis value for each numeric column
##################################
numeric_kurtosis_list = breast_cancer_numeric.kurtosis()

##################################
# Generating a column quality summary for the numeric column
##################################
numeric_column_quality_summary = pd.DataFrame(zip(numeric_variable_name_list,
                                                numeric_minimum_list,
                                                numeric_mean_list,
                                                numeric_median_list,
                                                numeric_maximum_list,
                                                numeric_first_mode_list,
                                                numeric_second_mode_list,
                                                numeric_first_mode_count_list,
                                                numeric_second_mode_count_list,
                                                numeric_first_second_mode_ratio_list,
                                                numeric_unique_count_list,
                                                numeric_row_count_list,
                                                numeric_unique_count_ratio_list,
                                                numeric_skewness_list,
                                                numeric_kurtosis_list), 
                                        columns=['Numeric.Column.Name',
                                                 'Minimum',
                                                 'Mean',
                                                 'Median',
                                                 'Maximum',
                                                 'First.Mode',
                                                 'Second.Mode',
                                                 'First.Mode.Count',
                                                 'Second.Mode.Count',
                                                 'First.Second.Mode.Ratio',
                                                 'Unique.Count',
                                                 'Row.Count',
                                                 'Unique.Count.Ratio',
                                                 'Skewness',
                                                 'Kurtosis'])
display(numeric_column_quality_summary)

	Numeric.Column.Name	Minimum	Mean	Median	Maximum	First.Mode	Second.Mode	First.Mode.Count	Second.Mode.Count	First.Second.Mode.Ratio	Unique.Count	Row.Count	Unique.Count.Ratio	Skewness	Kurtosis
0	radius_mean	6.981000	14.127292	13.370000	28.11000	12.340000	11.060000	4	3	1.333333	456	569	0.801406	0.942380	0.845522
1	texture_mean	9.710000	19.289649	18.840000	39.28000	16.840000	19.830000	3	3	1.000000	479	569	0.841828	0.650450	0.758319
2	perimeter_mean	43.790000	91.969033	86.240000	188.50000	82.610000	134.700000	3	3	1.000000	522	569	0.917399	0.990650	0.972214
3	area_mean	143.500000	654.889104	551.100000	2501.00000	512.200000	394.100000	3	2	1.500000	539	569	0.947276	1.645732	3.652303
4	smoothness_mean	0.052630	0.096360	0.095870	0.16340	0.100700	0.105400	5	4	1.250000	474	569	0.833040	0.456324	0.855975
5	compactness_mean	0.019380	0.104341	0.092630	0.34540	0.114700	0.120600	3	3	1.000000	537	569	0.943761	1.190123	1.650130
6	concavity_mean	0.000000	0.088799	0.061540	0.42680	0.000000	0.120400	13	3	4.333333	537	569	0.943761	1.401180	1.998638
7	concave points_mean	0.000000	0.048919	0.033500	0.20120	0.000000	0.028640	13	3	4.333333	542	569	0.952548	1.171180	1.066556
8	symmetry_mean	0.106000	0.181162	0.179200	0.30400	0.176900	0.189300	4	4	1.000000	432	569	0.759227	0.725609	1.287933
9	fractal_dimension_mean	0.049960	0.062798	0.061540	0.09744	0.067820	0.061130	3	3	1.000000	499	569	0.876977	1.304489	3.005892
10	radius_se	0.111500	0.405172	0.324200	2.87300	0.286000	0.220400	3	3	1.000000	540	569	0.949033	3.088612	17.686726
11	texture_se	0.360200	1.216853	1.108000	4.88500	0.856100	1.350000	3	3	1.000000	519	569	0.912127	1.646444	5.349169
12	perimeter_se	0.757000	2.866059	2.287000	21.98000	1.778000	1.143000	4	2	2.000000	533	569	0.936731	3.443615	21.401905
13	area_se	6.802000	40.337079	24.530000	542.20000	16.970000	16.640000	3	3	1.000000	528	569	0.927944	5.447186	49.209077
14	smoothness_se	0.001713	0.007041	0.006380	0.03113	0.005910	0.006064	2	2	1.000000	547	569	0.961336	2.314450	10.469840
15	compactness_se	0.002252	0.025478	0.020450	0.13540	0.018120	0.011040	3	3	1.000000	541	569	0.950791	1.902221	5.106252
16	concavity_se	0.000000	0.031894	0.025890	0.39600	0.000000	0.021850	13	2	6.500000	533	569	0.936731	5.110463	48.861395
17	concave points_se	0.000000	0.011796	0.010930	0.05279	0.000000	0.011670	13	3	4.333333	507	569	0.891037	1.444678	5.126302
18	symmetry_se	0.007882	0.020542	0.018730	0.07895	0.013440	0.020450	4	3	1.333333	498	569	0.875220	2.195133	7.896130
19	fractal_dimension_se	0.000895	0.003795	0.003187	0.02984	0.002256	0.002205	2	2	1.000000	545	569	0.957821	3.923969	26.280847
20	radius_worst	7.930000	16.269190	14.970000	36.04000	12.360000	13.500000	5	4	1.250000	457	569	0.803163	1.103115	0.944090
21	texture_worst	12.020000	25.677223	25.410000	49.54000	17.700000	27.260000	3	3	1.000000	511	569	0.898067	0.498321	0.224302
22	perimeter_worst	50.410000	107.261213	97.660000	251.20000	117.700000	105.900000	3	3	1.000000	514	569	0.903339	1.128164	1.070150
23	area_worst	185.200000	880.583128	686.500000	4254.00000	698.800000	808.900000	2	2	1.000000	544	569	0.956063	1.859373	4.396395
24	smoothness_worst	0.071170	0.132369	0.131300	0.22260	0.140100	0.131200	4	4	1.000000	411	569	0.722320	0.415426	0.517825
25	compactness_worst	0.027290	0.254265	0.211900	1.05800	0.148600	0.341600	3	3	1.000000	529	569	0.929701	1.473555	3.039288
26	concavity_worst	0.000000	0.272188	0.226700	1.25200	0.000000	0.450400	13	3	4.333333	539	569	0.947276	1.150237	1.615253
27	concave points_worst	0.000000	0.114606	0.099930	0.29100	0.000000	0.110500	13	3	4.333333	492	569	0.864675	0.492616	-0.535535
28	symmetry_worst	0.156500	0.290076	0.282200	0.66380	0.236900	0.310900	3	3	1.000000	500	569	0.878735	1.433928	4.444560
29	fractal_dimension_worst	0.055040	0.083946	0.080040	0.20750	0.074270	0.087010	3	2	1.500000	535	569	0.940246	1.662579	5.244611

##################################
# Counting the number of numeric columns
# with First.Second.Mode.Ratio > 5.00
##################################
len(numeric_column_quality_summary[(numeric_column_quality_summary['First.Second.Mode.Ratio']>10)])

0

##################################
# Counting the number of numeric columns
# with Unique.Count.Ratio > 10.00
##################################
len(numeric_column_quality_summary[(numeric_column_quality_summary['Unique.Count.Ratio']>10)])

0

#################################
# Counting the number of numeric columns
# with Skewness > 3.00 or Skewness < -3.00
##################################
len(numeric_column_quality_summary[(numeric_column_quality_summary['Skewness']>3) | (numeric_column_quality_summary['Skewness']<(-3))])

5

##################################
# Identifying the numerical columns
# with Skewness > 3.00 or Skewness < -3.00
##################################
display(numeric_column_quality_summary[(numeric_column_quality_summary['Skewness']>3) | (numeric_column_quality_summary['Skewness']<(-3))].sort_values(by=['Skewness'], ascending=False))

	Numeric.Column.Name	Minimum	Mean	Median	Maximum	First.Mode	Second.Mode	First.Mode.Count	Second.Mode.Count	First.Second.Mode.Ratio	Unique.Count	Row.Count	Unique.Count.Ratio	Skewness	Kurtosis
13	area_se	6.802000	40.337079	24.530000	542.20000	16.970000	16.640000	3	3	1.0	528	569	0.927944	5.447186	49.209077
16	concavity_se	0.000000	0.031894	0.025890	0.39600	0.000000	0.021850	13	2	6.5	533	569	0.936731	5.110463	48.861395
19	fractal_dimension_se	0.000895	0.003795	0.003187	0.02984	0.002256	0.002205	2	2	1.0	545	569	0.957821	3.923969	26.280847
12	perimeter_se	0.757000	2.866059	2.287000	21.98000	1.778000	1.143000	4	2	2.0	533	569	0.936731	3.443615	21.401905
10	radius_se	0.111500	0.405172	0.324200	2.87300	0.286000	0.220400	3	3	1.0	540	569	0.949033	3.088612	17.686726

##################################
# Formulating the dataset
# with categorical columns only
##################################
breast_cancer_categorical = breast_cancer.select_dtypes(include=['category','object'])

##################################
# Gathering the variable names for the categorical column
##################################
categorical_variable_name_list = breast_cancer_categorical.columns

##################################
# Gathering the first mode values for each categorical column
##################################
categorical_first_mode_list = [breast_cancer[x].value_counts().index.tolist()[0] for x in breast_cancer_categorical]

##################################
# Gathering the second mode values for each categorical column
##################################
categorical_second_mode_list = [breast_cancer[x].value_counts().index.tolist()[1] for x in breast_cancer_categorical]

##################################
# Gathering the count of first mode values for each categorical column
##################################
categorical_first_mode_count_list = [breast_cancer_categorical[x].isin([breast_cancer[x].value_counts(dropna=True).index.tolist()[0]]).sum() for x in breast_cancer_categorical]

##################################
# Gathering the count of second mode values for each categorical column
##################################
categorical_second_mode_count_list = [breast_cancer_categorical[x].isin([breast_cancer[x].value_counts(dropna=True).index.tolist()[1]]).sum() for x in breast_cancer_categorical]

##################################
# Gathering the first mode to second mode ratio for each categorical column
##################################
categorical_first_second_mode_ratio_list = map(truediv, categorical_first_mode_count_list, categorical_second_mode_count_list)

##################################
# Gathering the count of unique values for each categorical column
##################################
categorical_unique_count_list = breast_cancer_categorical.nunique(dropna=True)

##################################
# Gathering the number of observations for each categorical column
##################################
categorical_row_count_list = list([len(breast_cancer_categorical)] * len(breast_cancer_categorical.columns))

##################################
# Gathering the unique to count ratio for each categorical column
##################################
categorical_unique_count_ratio_list = map(truediv, categorical_unique_count_list, categorical_row_count_list)

##################################
# Generating a column quality summary for the categorical columns
##################################
categorical_column_quality_summary = pd.DataFrame(zip(categorical_variable_name_list,
                                                    categorical_first_mode_list,
                                                    categorical_second_mode_list,
                                                    categorical_first_mode_count_list,
                                                    categorical_second_mode_count_list,
                                                    categorical_first_second_mode_ratio_list,
                                                    categorical_unique_count_list,
                                                    categorical_row_count_list,
                                                    categorical_unique_count_ratio_list), 
                                        columns=['Categorical.Column.Name',
                                                 'First.Mode',
                                                 'Second.Mode',
                                                 'First.Mode.Count',
                                                 'Second.Mode.Count',
                                                 'First.Second.Mode.Ratio',
                                                 'Unique.Count',
                                                 'Row.Count',
                                                 'Unique.Count.Ratio'])
display(categorical_column_quality_summary)

	Categorical.Column.Name	First.Mode	Second.Mode	First.Mode.Count	Second.Mode.Count	First.Second.Mode.Ratio	Unique.Count	Row.Count	Unique.Count.Ratio
0	diagnosis	B	M	357	212	1.683962	2	569	0.003515

##################################
# Counting the number of categorical columns
# with First.Second.Mode.Ratio > 5.00
##################################
len(categorical_column_quality_summary[(categorical_column_quality_summary['First.Second.Mode.Ratio']>5)])

0

##################################
# Counting the number of categorical columns
# with Unique.Count.Ratio > 10.00
##################################
len(categorical_column_quality_summary[(categorical_column_quality_summary['Unique.Count.Ratio']>10)])

0

1.4. Data Preprocessing

1.4.1 Data Splitting

1. The baseline dataset is comprised of:
   • 569 rows (observations)
     • 357 diagnosis=B: 62.74%
     • 212 diagnosis=M: 37.26%
   • 31 columns (variables)
     • 1/31 target (categorical)
       • diagnosis
     • 30/31 predictor (numeric)
       • radius_mean
       • texture_mean
       • perimeter_mean
       • area_mean
       • smoothness_mean
       • compactness_mean
       • concavity_mean
       • concave points_mean
       • symmetry_mean
       • fractal_dimension_mean
       • radius_se
       • texture_se
       • perimeter_se
       • area_se
       • smoothness_se
       • compactness_se
       • concavity_se
       • concave points_se
       • symmetry_se
       • fractal_dimension_se
       • radius_worst
       • texture_worst
       • perimeter_worst
       • area_worst
       • smoothness_worst
       • compactness_worst
       • concavity_worst
       • concave points_worst
       • symmetry_worst
       • fractal_dimension_worst
2. The baseline dataset was divided into three subsets using a fixed random seed:
   • test data: 25% of the original data with class stratification applied
   • train data (initial): 75% of the original data with class stratification applied
     • train data (final): 75% of the train (initial) data with class stratification applied
     • validation data: 25% of the train (initial) data with class stratification applied
3. Models were developed from the train data (final). Using the same dataset, a subset of models with optimal hyperparameters were selected, based on cross-validation.
4. Among candidate models with optimal hyperparameters, the final model was selected based on performance on the validation data.
5. Performance of the selected final model (and other candidate models for post-model selection comparison) were evaluated using the test data.
6. The train data (final) subset is comprised of:
   • 319 rows (observations)
     • 200 diagnosis=B: 62.69%
     • 119 diagnosis=M: 37.30%
   • 31 columns (variables)
7. The validation data subset is comprised of:
   • 107 rows (observations)
     • 67 diagnosis=B: 62.61%
     • 40 diagnosis=M: 37.38%
   • 31 columns (variables)
8. The test data subset is comprised of:
   • 143 rows (observations)
     • 90 diagnosis=B: 62.93%
     • 53 diagnosis=M: 37.06%
   • 31 columns (variables)

##################################
# Creating a dataset copy
# of the original data
##################################
breast_cancer_baseline = breast_cancer.copy()

##################################
# Performing a general exploration
# of the baseline dataset
##################################
print('Final Dataset Dimensions: ')
display(breast_cancer_baseline.shape)

Final Dataset Dimensions: 

(569, 31)

##################################
# Obtaining the distribution of
# of the target variable
##################################
print('Target Variable Breakdown: ')
breast_cancer_breakdown = breast_cancer_baseline.groupby('diagnosis', observed=True).size().reset_index(name='Count')
breast_cancer_breakdown['Percentage'] = (breast_cancer_breakdown['Count'] / len(breast_cancer_baseline)) * 100
display(breast_cancer_breakdown)

Target Variable Breakdown: 

	diagnosis	Count	Percentage
0	B	357	62.741652
1	M	212	37.258348

##################################
# Formulating the train and test data
# from the final dataset
# by applying stratification and
# using a 75-25 ratio
##################################
breast_cancer_train_initial, breast_cancer_test = train_test_split(breast_cancer_baseline, 
                                                               test_size=0.25, 
                                                               stratify=breast_cancer_baseline['diagnosis'], 
                                                               random_state=987654321)

##################################
# Performing a general exploration
# of the initial training dataset
##################################
X_train_initial = breast_cancer_train_initial.drop('diagnosis', axis = 1)
y_train_initial = breast_cancer_train_initial['diagnosis']
print('Initial Train Dataset Dimensions: ')
display(X_train_initial.shape)
display(y_train_initial.shape)
print('Initial Train Target Variable Breakdown: ')
display(y_train_initial.value_counts())
print('Initial Train Target Variable Proportion: ')
display(y_train_initial.value_counts(normalize = True))

Initial Train Dataset Dimensions: 

(426, 30)

(426,)

Initial Train Target Variable Breakdown: 

diagnosis
B    267
M    159
Name: count, dtype: int64

Initial Train Target Variable Proportion: 

diagnosis
B    0.626761
M    0.373239
Name: proportion, dtype: float64

##################################
# Performing a general exploration
# of the test dataset
##################################
X_test = breast_cancer_test.drop('diagnosis', axis = 1)
y_test = breast_cancer_test['diagnosis']
print('Test Dataset Dimensions: ')
display(X_test.shape)
display(y_test.shape)
print('Test Target Variable Breakdown: ')
display(y_test.value_counts())
print('Test Target Variable Proportion: ')
display(y_test.value_counts(normalize = True))

Test Dataset Dimensions: 

(143, 30)

(143,)

Test Target Variable Breakdown: 

diagnosis
B    90
M    53
Name: count, dtype: int64

Test Target Variable Proportion: 

diagnosis
B    0.629371
M    0.370629
Name: proportion, dtype: float64

##################################
# Formulating the train and validation data
# from the train dataset
# by applying stratification and
# using a 75-25 ratio
##################################
breast_cancer_train, breast_cancer_validation = train_test_split(breast_cancer_train_initial, 
                                                             test_size=0.25, 
                                                             stratify=breast_cancer_train_initial['diagnosis'], 
                                                             random_state=987654321)

##################################
# Performing a general exploration
# of the final training dataset
##################################
X_train = breast_cancer_train.drop('diagnosis', axis = 1)
y_train = breast_cancer_train['diagnosis']
print('Final Train Dataset Dimensions: ')
display(X_train.shape)
display(y_train.shape)
print('Final Train Target Variable Breakdown: ')
display(y_train.value_counts())
print('Final Train Target Variable Proportion: ')
display(y_train.value_counts(normalize = True))

Final Train Dataset Dimensions: 

(319, 30)

(319,)

Final Train Target Variable Breakdown: 

diagnosis
B    200
M    119
Name: count, dtype: int64

Final Train Target Variable Proportion: 

diagnosis
B    0.626959
M    0.373041
Name: proportion, dtype: float64

##################################
# Performing a general exploration
# of the validation dataset
##################################
X_validation = breast_cancer_validation.drop('diagnosis', axis = 1)
y_validation = breast_cancer_validation['diagnosis']
print('Validation Dataset Dimensions: ')
display(X_validation.shape)
display(y_validation.shape)
print('Validation Target Variable Breakdown: ')
display(y_validation.value_counts())
print('Validation Target Variable Proportion: ')
display(y_validation.value_counts(normalize = True))

Validation Dataset Dimensions: 

(107, 30)

(107,)

Validation Target Variable Breakdown: 

diagnosis
B    67
M    40
Name: count, dtype: int64

Validation Target Variable Proportion: 

diagnosis
B    0.626168
M    0.373832
Name: proportion, dtype: float64

##################################
# Saving the training data
# to the DATASETS_FINAL_TRAIN_PATH
# and DATASETS_FINAL_TRAIN_FEATURES_PATH
# and DATASETS_FINAL_TRAIN_TARGET_PATH
##################################
breast_cancer_train.to_csv(os.path.join("..", DATASETS_FINAL_TRAIN_PATH, "breast_cancer_train.csv"), index=False)
X_train.to_csv(os.path.join("..", DATASETS_FINAL_TRAIN_FEATURES_PATH, "X_train.csv"), index=False)
y_train.to_csv(os.path.join("..", DATASETS_FINAL_TRAIN_TARGET_PATH, "y_train.csv"), index=False)

##################################
# Saving the validation data
# to the DATASETS_FINAL_VALIDATION_PATH
# and DATASETS_FINAL_VALIDATION_FEATURE_PATH
# and DATASETS_FINAL_VALIDATION_TARGET_PATH
##################################
breast_cancer_validation.to_csv(os.path.join("..", DATASETS_FINAL_VALIDATION_PATH, "breast_cancer_validation.csv"), index=False)
X_validation.to_csv(os.path.join("..", DATASETS_FINAL_VALIDATION_FEATURES_PATH, "X_validation.csv"), index=False)
y_validation.to_csv(os.path.join("..", DATASETS_FINAL_VALIDATION_TARGET_PATH, "y_validation.csv"), index=False)

##################################
# Saving the test data
# to the DATASETS_FINAL_TEST_PATH
# and DATASETS_FINAL_TEST_FEATURES_PATH
# and DATASETS_FINAL_TEST_TARGET_PATH
##################################
breast_cancer_test.to_csv(os.path.join("..", DATASETS_FINAL_TEST_PATH, "breast_cancer_test.csv"), index=False)
X_test.to_csv(os.path.join("..", DATASETS_FINAL_TEST_FEATURES_PATH, "X_test.csv"), index=False)
y_test.to_csv(os.path.join("..", DATASETS_FINAL_TEST_TARGET_PATH, "y_test.csv"), index=False)

1.4.2 Outlier and Distributional Shape Analysis

Outlier and distributional shape analysis findings based on assessment of the training data are as follows:

1. High skewness observed for 5 variables with Skewness>3 or Skewness<(-3).
   • area_se: Skewness = 6.562
   • concavity_se: Skewness = 5.648
   • fractal_dimension_se: Skewness = 4.280
   • perimeter_se: Skewness = 4.136
   • radius_se: Skewness = 3.775
2. Relatively high number of outliers observed for 7 numeric variables with Outlier.Ratio>0.05.
   • area_se: Outlier.Ratio = 0.110
   • radius_se: Outlier.Ratio = 0.075
   • perimeter_se: Outlier.Ratio = 0.075
   • smoothness_se: Outlier.Ratio = 0.059
   • compactness_se: Outlier.Ratio = 0.059
   • fractal_dimension_se: Outlier.Ratio = 0.056
   • symmetry_se: Outlier.Ratio = 0.050

##################################
# Formulating the training dataset
# with numeric columns only
##################################
breast_cancer_train_numeric = breast_cancer_train.select_dtypes(include='number')

##################################
# Gathering the variable names for each numeric column
##################################
numeric_variable_name_list = list(breast_cancer_train_numeric.columns)

##################################
# Gathering the skewness value for each numeric column
##################################
numeric_skewness_list = breast_cancer_train_numeric.skew()

##################################
# Computing the interquartile range
# for all columns
##################################
breast_cancer_train_numeric_q1 = breast_cancer_train_numeric.quantile(0.25)
breast_cancer_train_numeric_q3 = breast_cancer_train_numeric.quantile(0.75)
breast_cancer_train_numeric_iqr = breast_cancer_train_numeric_q3 - breast_cancer_train_numeric_q1

##################################
# Gathering the outlier count for each numeric column
# based on the interquartile range criterion
##################################
numeric_outlier_count_list = ((breast_cancer_train_numeric < (breast_cancer_train_numeric_q1 - 1.5 * breast_cancer_train_numeric_iqr)) | (breast_cancer_train_numeric > (breast_cancer_train_numeric_q3 + 1.5 * breast_cancer_train_numeric_iqr))).sum()

##################################
# Gathering the number of observations for each column
##################################
numeric_row_count_list = list([len(breast_cancer_train_numeric)] * len(breast_cancer_train_numeric.columns))

##################################
# Gathering the unique to count ratio for each categorical column
##################################
numeric_outlier_ratio_list = map(truediv, numeric_outlier_count_list, numeric_row_count_list)

##################################
# Formulating the outlier summary
# for all numeric columns
##################################
numeric_column_outlier_summary = pd.DataFrame(zip(numeric_variable_name_list,
                                                  numeric_skewness_list,
                                                  numeric_outlier_count_list,
                                                  numeric_row_count_list,
                                                  numeric_outlier_ratio_list), 
                                        columns=['Numeric.Column.Name',
                                                 'Skewness',
                                                 'Outlier.Count',
                                                 'Row.Count',
                                                 'Outlier.Ratio'])
display(numeric_column_outlier_summary)

	Numeric.Column.Name	Skewness	Outlier.Count	Row.Count	Outlier.Ratio
0	radius_mean	0.966211	6	319	0.018809
1	texture_mean	0.746964	4	319	0.012539
2	perimeter_mean	1.034320	6	319	0.018809
3	area_mean	1.819687	9	319	0.028213
4	smoothness_mean	0.166009	1	319	0.003135
5	compactness_mean	1.115958	6	319	0.018809
6	concavity_mean	1.412274	10	319	0.031348
7	concave points_mean	1.155582	11	319	0.034483
8	symmetry_mean	0.532891	7	319	0.021944
9	fractal_dimension_mean	1.054941	8	319	0.025078
10	radius_se	3.775498	24	319	0.075235
11	texture_se	1.464707	10	319	0.031348
12	perimeter_se	4.136225	24	319	0.075235
13	area_se	6.562034	35	319	0.109718
14	smoothness_se	1.313172	19	319	0.059561
15	compactness_se	1.701432	19	319	0.059561
16	concavity_se	5.648674	14	319	0.043887
17	concave points_se	1.592173	14	319	0.043887
18	symmetry_se	2.442436	16	319	0.050157
19	fractal_dimension_se	4.280973	18	319	0.056426
20	radius_worst	1.016127	3	319	0.009404
21	texture_worst	0.476084	2	319	0.006270
22	perimeter_worst	1.075965	5	319	0.015674
23	area_worst	1.892646	13	319	0.040752
24	smoothness_worst	0.237077	0	319	0.000000
25	compactness_worst	1.098476	6	319	0.018809
26	concavity_worst	1.067913	5	319	0.015674
27	concave points_worst	0.436446	0	319	0.000000
28	symmetry_worst	1.154060	10	319	0.031348
29	fractal_dimension_worst	1.001579	10	319	0.031348

##################################
# Identifying the numerical columns
# with Skewness > 3.00 or Skewness < -3.00
##################################
display(numeric_column_outlier_summary[(numeric_column_outlier_summary['Skewness']>3) | (numeric_column_outlier_summary['Skewness']<(-3))].sort_values(by=['Skewness'], ascending=False))

	Numeric.Column.Name	Skewness	Outlier.Count	Row.Count	Outlier.Ratio
13	area_se	6.562034	35	319	0.109718
16	concavity_se	5.648674	14	319	0.043887
19	fractal_dimension_se	4.280973	18	319	0.056426
12	perimeter_se	4.136225	24	319	0.075235
10	radius_se	3.775498	24	319	0.075235

##################################
# Identifying the numerical columns
# with Outlier.Ratio > 0.05
##################################
display(numeric_column_outlier_summary[numeric_column_outlier_summary['Outlier.Ratio']>0.05].sort_values(by=['Outlier.Ratio'], ascending=False))

	Numeric.Column.Name	Skewness	Outlier.Count	Row.Count	Outlier.Ratio
13	area_se	6.562034	35	319	0.109718
10	radius_se	3.775498	24	319	0.075235
12	perimeter_se	4.136225	24	319	0.075235
14	smoothness_se	1.313172	19	319	0.059561
15	compactness_se	1.701432	19	319	0.059561
19	fractal_dimension_se	4.280973	18	319	0.056426
18	symmetry_se	2.442436	16	319	0.050157

##################################
# Formulating the individual boxplots
# for all numeric columns
##################################
for column in breast_cancer_train_numeric:
        plt.figure(figsize=(17,1))
        sns.boxplot(data=breast_cancer_train_numeric, x=column)
        plt.show()
        plt.close()

1.4.3 Collinearity

Collinearity evaluation findings based on assessment of the training data are as follows:

1. Predictors were predominantly positively correlated with 50% reporting correlation values ranging from 0.129 to 0.558.
2. High Pearson.Correlation values > 0.90 were noted for 4.60% (20/435) of the pairwise combinations of predictors:
   • radius_mean and perimeter_mean: Pearson.Correlation = 0.997
   • radius_worst and perimeter_worst: Pearson.Correlation = 0.993
   • perimeter_mean and area_mean: Pearson.Correlation = 0.985
   • radius_mean and area_mean: Pearson.Correlation = 0.984
   • radius_worst and area_worst: Pearson.Correlation = 0.982
   • perimeter_worst and area_worst: Pearson.Correlation = 0.978
   • perimeter_mean and perimeter_worst: Pearson.Correlation = 0.972
   • perimeter_mean and radius_worst: Pearson.Correlation = 0.972
   • radius_mean and radius_worst: Pearson.Correlation = 0.971
   • radius_se and perimeter_se: Pearson.Correlation = 0.971
   • radius_mean and perimeter_worst: Pearson.Correlation = 0.967
   • area_mean and area_worst: Pearson.Correlation = 0.964
   • area_mean and radius_worst: Pearson.Correlation = 0.958
   • area_mean and perimeter_worst: Pearson.Correlation = 0.955
   • perimeter_mean and area_worst: Pearson.Correlation = 0.951
   • radius_se and area_se: Pearson.Correlation = 0.948
   • radius_mean and area_worst: Pearson.Correlation = 0.948
   • perimeter_se and area_se: Pearson.Correlation = 0.942
   • texture_mean and texture_worst: Pearson.Correlation = 0.923
   • concave points_mean and concave points_worst: Pearson.Correlation = 0.911
   • concavity_mean and concave points_mean: Pearson.Correlation = 0.900

##################################
# Creating a dataset copy
# with only the predictors present
# for correlation analysis
##################################
breast_cancer_train_correlation = breast_cancer_train.drop(['diagnosis'], axis=1)
display(breast_cancer_train_correlation)

	radius_mean	texture_mean	perimeter_mean	area_mean	smoothness_mean	compactness_mean	concavity_mean	concave points_mean	symmetry_mean	fractal_dimension_mean	...	radius_worst	texture_worst	perimeter_worst	area_worst	smoothness_worst	compactness_worst	concavity_worst	concave points_worst	symmetry_worst	fractal_dimension_worst
id
868826	14.950	17.57	96.85	678.1	0.11670	0.13050	0.15390	0.08624	0.1957	0.06216	...	18.55	21.43	121.40	971.4	0.1411	0.21640	0.33550	0.16670	0.3414	0.07147
8810703	28.110	18.47	188.50	2499.0	0.11420	0.15160	0.32010	0.15950	0.1648	0.05525	...	28.11	18.47	188.50	2499.0	0.1142	0.15160	0.32010	0.15950	0.1648	0.05525
906878	13.660	19.13	89.46	575.3	0.09057	0.11470	0.09657	0.04812	0.1848	0.06181	...	15.14	25.50	101.40	708.8	0.1147	0.31670	0.36600	0.14070	0.2744	0.08839
911654	14.200	20.53	92.41	618.4	0.08931	0.11080	0.05063	0.03058	0.1506	0.06009	...	16.45	27.26	112.10	828.5	0.1153	0.34290	0.25120	0.13390	0.2534	0.07858
903483	8.734	16.84	55.27	234.3	0.10390	0.07428	0.00000	0.00000	0.1985	0.07098	...	10.17	22.80	64.01	317.0	0.1460	0.13100	0.00000	0.00000	0.2445	0.08865
...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...
84862001	16.130	20.68	108.10	798.8	0.11700	0.20220	0.17220	0.10280	0.2164	0.07356	...	20.96	31.48	136.80	1315.0	0.1789	0.42330	0.47840	0.20730	0.3706	0.11420
90317302	10.260	12.22	65.75	321.6	0.09996	0.07542	0.01923	0.01968	0.1800	0.06569	...	11.38	15.65	73.23	394.5	0.1343	0.16500	0.08615	0.06696	0.2937	0.07722
86211	12.180	17.84	77.79	451.1	0.10450	0.07057	0.02490	0.02941	0.1900	0.06635	...	12.83	20.92	82.14	495.2	0.1140	0.09358	0.04980	0.05882	0.2227	0.07376
926954	16.600	28.08	108.30	858.1	0.08455	0.10230	0.09251	0.05302	0.1590	0.05648	...	18.98	34.12	126.70	1124.0	0.1139	0.30940	0.34030	0.14180	0.2218	0.07820
86208	20.260	23.03	132.40	1264.0	0.09078	0.13130	0.14650	0.08683	0.2095	0.05649	...	24.22	31.59	156.10	1750.0	0.1190	0.35390	0.40980	0.15730	0.3689	0.08368

319 rows × 30 columns

##################################
# Initializing the correlation matrix
##################################
breast_cancer_train_correlation_matrix = pd.DataFrame(np.zeros((len(breast_cancer_train_correlation.columns), len(breast_cancer_train_correlation.columns))),
                                                       columns=breast_cancer_train_correlation.columns,
                                                       index=breast_cancer_train_correlation.columns)

##################################
# Calculating different types
# of correlation coefficients
# per variable type
##################################
for i in range(len(breast_cancer_train_correlation.columns)):
    for j in range(i, len(breast_cancer_train_correlation.columns)):
        if i == j:
            breast_cancer_train_correlation_matrix.iloc[i, j] = 1.0  
        else:
            col_i = breast_cancer_train_correlation.iloc[:, i]
            col_j = breast_cancer_train_correlation.iloc[:, j]

            # Detecting binary variables (assumes binary variables are coded as 0/1)
            is_binary_i = col_i.nunique() == 2
            is_binary_j = col_j.nunique() == 2

            # Computing the Pearson correlation for two continuous variables
            if col_i.dtype in ['int64', 'float64'] and col_j.dtype in ['int64', 'float64']:
                corr = col_i.corr(col_j)

            # Computing the Point-Biserial correlation for continuous and binary variables
            elif (col_i.dtype in ['int64', 'float64'] and is_binary_j) or (col_j.dtype in ['int64', 'float64'] and is_binary_i):
                continuous_var = col_i if col_i.dtype in ['int64', 'float64'] else col_j
                binary_var = col_j if is_binary_j else col_i

                # Convert binary variable to 0/1 (if not already)
                binary_var = binary_var.astype('category').cat.codes
                corr, _ = pointbiserialr(continuous_var, binary_var)

            # Computing the Phi coefficient for two binary variables
            elif is_binary_i and is_binary_j:
                corr = col_i.corr(col_j) 

            # Computing the Cramér's V for two categorical variables (if more than 2 categories)
            else:
                contingency_table = pd.crosstab(col_i, col_j)
                chi2, _, _, _ = chi2_contingency(contingency_table)
                n = contingency_table.sum().sum()
                phi2 = chi2 / n
                r, k = contingency_table.shape
                corr = np.sqrt(phi2 / min(k - 1, r - 1))  # Cramér's V formula

            # Assigning correlation values to the matrix
            breast_cancer_train_correlation_matrix.iloc[i, j] = corr
            breast_cancer_train_correlation_matrix.iloc[j, i] = corr
            # Displaying the correlation matrix
display(breast_cancer_train_correlation_matrix)

	radius_mean	texture_mean	perimeter_mean	area_mean	smoothness_mean	compactness_mean	concavity_mean	concave points_mean	symmetry_mean	fractal_dimension_mean	...	radius_worst	texture_worst	perimeter_worst	area_worst	smoothness_worst	compactness_worst	concavity_worst	concave points_worst	symmetry_worst	fractal_dimension_worst
radius_mean	1.000000	0.296754	0.997917	0.984916	0.145069	0.521699	0.653960	0.829568	0.178392	-0.362551	...	0.971938	0.289640	0.967088	0.948294	0.072870	0.428210	0.496566	0.737347	0.217375	-0.038225
texture_mean	0.296754	1.000000	0.300384	0.293404	-0.081253	0.194167	0.243735	0.250668	0.068573	-0.098025	...	0.319664	0.923246	0.322248	0.312728	0.004546	0.214524	0.207238	0.222253	0.068177	0.054058
perimeter_mean	0.997917	0.300384	1.000000	0.985186	0.180173	0.570667	0.691792	0.855888	0.209569	-0.313834	...	0.972461	0.293613	0.972875	0.951121	0.103165	0.468946	0.531674	0.762926	0.235097	0.006081
area_mean	0.984916	0.293404	0.985186	1.000000	0.155662	0.519067	0.673052	0.829811	0.177404	-0.320518	...	0.958283	0.275844	0.955452	0.964157	0.080662	0.406863	0.489149	0.712358	0.188049	-0.033382
smoothness_mean	0.145069	-0.081253	0.180173	0.155662	1.000000	0.618184	0.497254	0.538361	0.530327	0.518288	...	0.197350	-0.022554	0.220016	0.198870	0.792618	0.414057	0.397902	0.487924	0.337613	0.444924
compactness_mean	0.521699	0.194167	0.570667	0.519067	0.618184	1.000000	0.878930	0.834485	0.586311	0.503176	...	0.558509	0.206030	0.612310	0.546968	0.515692	0.862123	0.797969	0.821965	0.453133	0.659234
concavity_mean	0.653960	0.243735	0.691792	0.673052	0.497254	0.878930	1.000000	0.900196	0.510785	0.329362	...	0.675255	0.253589	0.714621	0.683360	0.417894	0.751441	0.886489	0.851058	0.397756	0.514930
concave points_mean	0.829568	0.250668	0.855888	0.829811	0.538361	0.834485	0.900196	1.000000	0.454541	0.108612	...	0.846434	0.268006	0.868059	0.835507	0.422292	0.668006	0.723963	0.911806	0.374473	0.331439
symmetry_mean	0.178392	0.068573	0.209569	0.177404	0.530327	0.586311	0.510785	0.454541	1.000000	0.419840	...	0.220408	0.083343	0.247568	0.214373	0.412629	0.476576	0.453587	0.439723	0.689259	0.420701
fractal_dimension_mean	-0.362551	-0.098025	-0.313834	-0.320518	0.518288	0.503176	0.329362	0.108612	0.419840	1.000000	...	-0.307089	-0.093992	-0.258932	-0.270836	0.447918	0.394331	0.327619	0.123832	0.196195	0.759504
radius_se	0.658347	0.229739	0.669725	0.719571	0.280807	0.473529	0.591306	0.661259	0.267726	-0.028843	...	0.679356	0.147109	0.678844	0.727147	0.080241	0.249196	0.326790	0.483566	0.057317	0.006544
texture_se	-0.063347	0.436088	-0.053460	-0.035532	0.067398	0.045054	0.074459	0.026147	0.063259	0.175273	...	-0.083551	0.452090	-0.077713	-0.060645	-0.103064	-0.130696	-0.092730	-0.120547	-0.195414	-0.054273
perimeter_se	0.663993	0.235670	0.681743	0.726247	0.277255	0.528764	0.621664	0.679461	0.276983	0.009488	...	0.669812	0.153531	0.688770	0.718316	0.069734	0.309735	0.366793	0.510473	0.065297	0.048577
area_se	0.696051	0.210780	0.705619	0.774018	0.219236	0.429172	0.573166	0.643176	0.197534	-0.112437	...	0.699869	0.139774	0.702817	0.771195	0.061473	0.249041	0.328935	0.479149	0.041415	-0.023982
smoothness_se	-0.282663	-0.026715	-0.262615	-0.208247	0.309776	0.093602	0.069748	-0.028748	0.132195	0.446319	...	-0.281678	-0.113239	-0.270776	-0.216902	0.305564	-0.101057	-0.080945	-0.155433	-0.184909	0.113992
compactness_se	0.161000	0.116722	0.204162	0.180221	0.233059	0.706181	0.646702	0.440636	0.377026	0.595560	...	0.166451	0.053456	0.222276	0.182170	0.131374	0.632269	0.608224	0.448014	0.163800	0.599360
concavity_se	0.101351	0.044926	0.132131	0.129111	0.203394	0.508586	0.664396	0.354830	0.340789	0.506201	...	0.107206	0.007025	0.142656	0.128633	0.123140	0.429350	0.652703	0.382299	0.170189	0.461893
concave points_se	0.338116	0.079973	0.368434	0.339009	0.362823	0.650154	0.690708	0.591120	0.374946	0.383054	...	0.330233	0.012760	0.363817	0.327707	0.160674	0.451405	0.556709	0.590946	0.107170	0.332135
symmetry_se	-0.020080	0.031838	-0.001422	0.014059	0.160089	0.209686	0.200530	0.120330	0.373312	0.267390	...	-0.055671	-0.059537	-0.041901	-0.037870	-0.070226	-0.020577	0.024522	-0.022468	0.320748	-0.020828
fractal_dimension_se	-0.086706	-0.004000	-0.051803	-0.054896	0.200008	0.457416	0.433186	0.204754	0.284368	0.698610	...	-0.077667	-0.064249	-0.042828	-0.050680	0.086398	0.336647	0.354796	0.174112	0.015405	0.582141
radius_worst	0.971938	0.319664	0.972461	0.958283	0.197350	0.558509	0.675255	0.846434	0.220408	-0.307089	...	1.000000	0.341791	0.993610	0.982412	0.175453	0.494388	0.550967	0.788192	0.294281	0.050938
texture_worst	0.289640	0.923246	0.293613	0.275844	-0.022554	0.206030	0.253589	0.268006	0.083343	-0.093992	...	0.341791	1.000000	0.345039	0.323485	0.145721	0.290799	0.277103	0.299552	0.189918	0.139916
perimeter_worst	0.967088	0.322248	0.972875	0.955452	0.220016	0.612310	0.714621	0.868059	0.247568	-0.258932	...	0.993610	0.345039	1.000000	0.978668	0.196497	0.553308	0.597206	0.816546	0.310463	0.104998
area_worst	0.948294	0.312728	0.951121	0.964157	0.198870	0.546968	0.683360	0.835507	0.214373	-0.270836	...	0.982412	0.323485	0.978668	1.000000	0.174507	0.467797	0.537041	0.755701	0.258457	0.050037
smoothness_worst	0.072870	0.004546	0.103165	0.080662	0.792618	0.515692	0.417894	0.422292	0.412629	0.447918	...	0.175453	0.145721	0.196497	0.174507	1.000000	0.513382	0.478523	0.506041	0.446709	0.579201
compactness_worst	0.428210	0.214524	0.468946	0.406863	0.414057	0.862123	0.751441	0.668006	0.476576	0.394331	...	0.494388	0.290799	0.553308	0.467797	0.513382	1.000000	0.869064	0.805226	0.555227	0.782035
concavity_worst	0.496566	0.207238	0.531674	0.489149	0.397902	0.797969	0.886489	0.723963	0.453587	0.327619	...	0.550967	0.277103	0.597206	0.537041	0.478523	0.869064	1.000000	0.834462	0.510184	0.666844
concave points_worst	0.737347	0.222253	0.762926	0.712358	0.487924	0.821965	0.851058	0.911806	0.439723	0.123832	...	0.788192	0.299552	0.816546	0.755701	0.506041	0.805226	0.834462	1.000000	0.496234	0.478328
symmetry_worst	0.217375	0.068177	0.235097	0.188049	0.337613	0.453133	0.397756	0.374473	0.689259	0.196195	...	0.294281	0.189918	0.310463	0.258457	0.446709	0.555227	0.510184	0.496234	1.000000	0.427291
fractal_dimension_worst	-0.038225	0.054058	0.006081	-0.033382	0.444924	0.659234	0.514930	0.331439	0.420701	0.759504	...	0.050938	0.139916	0.104998	0.050037	0.579201	0.782035	0.666844	0.478328	0.427291	1.000000

30 rows × 30 columns

##################################
# Plotting the correlation matrix
# for all pairwise combinations
# of numeric columns
##################################
plt.figure(figsize=(25, 12))
sns.heatmap(breast_cancer_train_correlation_matrix, annot=True, cmap='coolwarm', vmin=-1, vmax=1)
plt.show()

##################################
# Formulating the pairwise correlation summary
# between the predictor columns
##################################
# Converting the correlation matrix to a long format
breast_cancer_train_correlation_summary = (
    breast_cancer_train_correlation_matrix
    # keeping the upper triangle of the correlation matrix
    .where(~np.tril(np.ones(breast_cancer_train_correlation_matrix.shape)).astype(bool))  
    # convering to a long format
    .stack()  
    .reset_index()
)

# Renaming the summary columns
breast_cancer_train_correlation_summary.columns = ['Predictor1.Column.Name', 'Predictor2.Column.Name', 'Pearson.Correlation']

# Sorting from highest to lowest
breast_cancer_train_correlation_summary = breast_cancer_train_correlation_summary.sort_values(by='Pearson.Correlation', ascending=False).reset_index(drop=True)

# Displaying the summary table
display(breast_cancer_train_correlation_summary)

	Predictor1.Column.Name	Predictor2.Column.Name	Pearson.Correlation
0	radius_mean	perimeter_mean	0.997917
1	radius_worst	perimeter_worst	0.993610
2	perimeter_mean	area_mean	0.985186
3	radius_mean	area_mean	0.984916
4	radius_worst	area_worst	0.982412
...	...	...	...
430	radius_mean	smoothness_se	-0.282663
431	fractal_dimension_mean	radius_worst	-0.307089
432	perimeter_mean	fractal_dimension_mean	-0.313834
433	area_mean	fractal_dimension_mean	-0.320518
434	radius_mean	fractal_dimension_mean	-0.362551

435 rows × 3 columns

##################################
# Exploring the pairwise correlation values
# between the predictor columns
##################################
breast_cancer_train_correlation_exploration = (
    breast_cancer_train_correlation_matrix
    .where(~np.tril(np.ones(breast_cancer_train_correlation_matrix.shape)).astype(bool))
    .stack()
    .values
)

# Computing the quartiles and IQR
correlation_q1 = np.percentile(breast_cancer_train_correlation_exploration, 25)
correlation_q3 = np.percentile(breast_cancer_train_correlation_exploration, 75)
correlation_iqr = correlation_q3 - correlation_q1

print(f"Q1 (25th percentile): {correlation_q1:.3f}")
print(f"Q3 (75th percentile): {correlation_q3:.3f}")
print(f"IQR (Q3 - Q1): {correlation_iqr:.3f}")

Q1 (25th percentile): 0.129
Q3 (75th percentile): 0.558
IQR (Q3 - Q1): 0.429

##################################
# Determining the highly collinear predictors
# with Pearson Correlation > 0.90
##################################
breast_cancer_train_correlation_summary_highcollinearity = breast_cancer_train_correlation_summary[breast_cancer_train_correlation_summary['Pearson.Correlation'].abs() > 0.90].reset_index(drop=True)
display(breast_cancer_train_correlation_summary_highcollinearity)

	Predictor1.Column.Name	Predictor2.Column.Name	Pearson.Correlation
0	radius_mean	perimeter_mean	0.997917
1	radius_worst	perimeter_worst	0.993610
2	perimeter_mean	area_mean	0.985186
3	radius_mean	area_mean	0.984916
4	radius_worst	area_worst	0.982412
5	perimeter_worst	area_worst	0.978668
6	perimeter_mean	perimeter_worst	0.972875
7	perimeter_mean	radius_worst	0.972461
8	radius_mean	radius_worst	0.971938
9	radius_se	perimeter_se	0.971589
10	radius_mean	perimeter_worst	0.967088
11	area_mean	area_worst	0.964157
12	area_mean	radius_worst	0.958283
13	area_mean	perimeter_worst	0.955452
14	perimeter_mean	area_worst	0.951121
15	radius_se	area_se	0.948731
16	radius_mean	area_worst	0.948294
17	perimeter_se	area_se	0.942853
18	texture_mean	texture_worst	0.923246
19	concave points_mean	concave points_worst	0.911806
20	concavity_mean	concave points_mean	0.900196

1.5. Data Exploration

1.5.1 Exploratory Data Analysis

Exploratory data analysis findings are as follows:

1. Bivariate analysis identified individual predictors with generally positive association to the target variable based on visual inspection.
2. A total of 24 of 30 predictors demonstrated higher values that are associated with the diagnosis=M category as compared to measurements under the diagnosis=B category:
   • radius_mean
   • texture_mean
   • perimeter_mean
   • area_mean
   • compactness_mean
   • concavity_mean
   • concave points_mean
   • symmetry_mean
   • radius_se
   • perimeter_se
   • area_se
   • compactness_se
   • concave points_se
   • fractal_dimension_se
   • radius_worst
   • texture_worst
   • perimeter_worst
   • area_worst
   • smoothness_worst
   • compactness_worst
   • concavity_worst
   • concave points_worst
   • symmetry_worst
   • fractal_dimension_worst

##################################
# Segregating the target
# and predictor variables
##################################
breast_cancer_train_predictors_numeric = breast_cancer_train.iloc[:,1:].columns

##################################
# Gathering the variable names for each numeric column
##################################
numeric_variable_name_list = breast_cancer_train_predictors_numeric

##################################
# Segregating the target variable
# and numeric predictors
##################################
boxplot_y_variable = 'diagnosis'
boxplot_x_variables = numeric_variable_name_list.values

##################################
# Defining the number of 
# rows and columns for the subplots
##################################
num_rows = 10
num_cols = 3

##################################
# Formulating the subplot structure
##################################
fig, axes = plt.subplots(num_rows, num_cols, figsize=(20, 40))

##################################
# Flattening the multi-row and
# multi-column axes
##################################
axes = axes.ravel()

##################################
# Formulating the individual boxplots
# for all scaled numeric columns
##################################
for i, x_variable in enumerate(boxplot_x_variables):
    ax = axes[i]
    ax.boxplot([group[x_variable] for name, group in breast_cancer_train.groupby(boxplot_y_variable, observed=True)])
    ax.set_title(f'{boxplot_y_variable} Versus {x_variable}')
    ax.set_xlabel(boxplot_y_variable)
    ax.set_ylabel(x_variable)
    ax.set_xticks(range(1, len(breast_cancer_train[boxplot_y_variable].unique()) + 1), ['B', 'M'])

##################################
# Adjusting the subplot layout
##################################
plt.tight_layout()

##################################
# Presenting the subplots
##################################
plt.show()

1.5.2 Hypothesis Testing

1. The relationship between the numeric predictors to the diagnosis target variable was statistically evaluated using the following hypotheses:
   • Null: Difference in the means between groups B and M is equal to zero
   • Alternative: Difference in the means between groups B and M is not equal to zero
2. There is sufficient evidence to conclude of a statistically significant difference between the means of the numeric measurements obtained from B and M groups of the diagnosis target variable in 26 of the 30 numeric predictors given their high t-test statistic values with reported low p-values less than the significance level of 0.05.
   • perimeter_worst: T.Test.Statistic=-23.391, T.Test.PValue=0.000
   • radius_worst: T.Test.Statistic=-23.228, T.Test.PValue=0.000
   • concave points_worst: T.Test.Statistic=-21.365, T.Test.PValue=0.000
   • concave points_mean: T.Test.Statistic=-21.258, T.Test.PValue=0.000
   • area_worst: T.Test.Statistic=-20.310, T.Test.PValue=0.000
   • perimeter_mean: T.Test.Statistic=-20.086, T.Test.PValue=0.000
   • radius_mean: T.Test.Statistic=-19.510, T.Test.PValue=0.000
   • area_mean: T.Test.Statistic=-17.991, T.Test.PValue=0.000
   • concavity_mean: T.Test.Statistic=-15.314, T.Test.PValue=0.026
   • concavity_worst: T.Test.Statistic=-13.368, T.Test.PValue=0.000
   • compactness_mean: T.Test.Statistic=-12.647, T.Test.PValue=0.000
   • compactness_worst: T.Test.Statistic=-12.079, T.Test.PValue=0.000
   • radius_se: T.Test.Statistic=-11.532, T.Test.PValue=0.000
   • perimeter_se: T.Test.Statistic=-11.234, T.Test.PValue=0.000
   • area_se: T.Test.Statistic=-10.375, T.Test.PValue=0.000
   • symmetry_worst: T.Test.Statistic=-8.312, T.Test.PValue=0.000
   • texture_worst: T.Test.Statistic=-7.911, T.Test.PValue=0.000
   • smoothness_worst: T.Test.Statistic=-7.080, T.Test.PValue=0.000
   • texture_mean: T.Test.Statistic=-6.682, T.Test.PValue=0.000
   • concave points_se: T.Test.Statistic=-6.679, T.Test.PValue=0.000
   • symmetry_mean: T.Test.Statistic=-6.315, T.Test.PValue=0.000
   • smoothness_mean: T.Test.Statistic=-6.087, T.Test.PValue=0.000
   • fractal_dimension_worst: T.Test.Statistic=-4.740, T.Test.PValue=0.000
   • compactness_se: T.Test.Statistic=-3.733, T.Test.PValue=0.000
   • concavity_se: T.Test.Statistic=-2.703, T.Test.PValue=0.007
   • smoothness_se: T.Test.Statistic=+2.425, T.Test.PValue=0.015
3. Feature extraction using Principal Component Analysis was explored to address the high number of correlated predictors noted with high skewness and outlier ratio. The 30 predictors can be potentially reduced to just 10 uncorrelated principal components representing 95% of the original variance.
   • pc_1: Explained_Variance_Ratio=0.426, Cumulative_Explained_Variance=0.426
   • pc_2: Explained_Variance_Ratio=0.189, Cumulative_Explained_Variance=0.615
   • pc_3: Explained_Variance_Ratio=0.101, Cumulative_Explained_Variance=0.717
   • pc_4: Explained_Variance_Ratio=0.068, Cumulative_Explained_Variance=0.786
   • pc_5: Explained_Variance_Ratio=0.058, Cumulative_Explained_Variance=0.845
   • pc_6: Explained_Variance_Ratio=0.042, Cumulative_Explained_Variance=0.887
   • pc_7: Explained_Variance_Ratio=0.022, Cumulative_Explained_Variance=0.910
   • pc_8: Explained_Variance_Ratio=0.016, Cumulative_Explained_Variance=0.926
   • pc_9: Explained_Variance_Ratio=0.014, Cumulative_Explained_Variance=0.941
   • pc_10: Explained_Variance_Ratio=0.011, Cumulative_Explained_Variance=0.953
   • pc_11: Explained_Variance_Ratio=0.010, Cumulative_Explained_Variance=0.963
   • pc_12: Explained_Variance_Ratio=0.008, Cumulative_Explained_Variance=0.972
   • pc_13: Explained_Variance_Ratio=0.007, Cumulative_Explained_Variance=0.979
   • pc_14: Explained_Variance_Ratio=0.004, Cumulative_Explained_Variance=0.984
   • pc_15: Explained_Variance_Ratio=0.002, Cumulative_Explained_Variance=0.986
   • pc_16: Explained_Variance_Ratio=0.002, Cumulative_Explained_Variance=0.989
   • pc_17: Explained_Variance_Ratio=0.001, Cumulative_Explained_Variance=0.991
   • pc_18: Explained_Variance_Ratio=0.001, Cumulative_Explained_Variance=0.993
   • pc_19: Explained_Variance_Ratio=0.001, Cumulative_Explained_Variance=0.994
   • pc_20: Explained_Variance_Ratio=0.001, Cumulative_Explained_Variance=0.995
   • pc_21: Explained_Variance_Ratio=0.000, Cumulative_Explained_Variance=0.996
   • pc_22: Explained_Variance_Ratio=0.000, Cumulative_Explained_Variance=0.997
   • pc_23: Explained_Variance_Ratio=0.000, Cumulative_Explained_Variance=0.998
   • pc_24: Explained_Variance_Ratio=0.000, Cumulative_Explained_Variance=0.999
   • pc_25: Explained_Variance_Ratio=0.000, Cumulative_Explained_Variance=0.999
   • pc_26: Explained_Variance_Ratio=0.000, Cumulative_Explained_Variance=0.999
   • pc_27: Explained_Variance_Ratio=0.000, Cumulative_Explained_Variance=0.999
   • pc_28: Explained_Variance_Ratio=0.000, Cumulative_Explained_Variance=0.999
   • pc_29: Explained_Variance_Ratio=0.000, Cumulative_Explained_Variance=0.999
   • pc_30: Explained_Variance_Ratio=0.000, Cumulative_Explained_Variance=1.000
4. There is sufficient evidence to conclude of a statistically significant difference between the means of the principal component values obtained from B and M groups of the diagnosis target variable in 6 of the 30 principal component predictors given their high t-test statistic values with reported low p-values less than the significance level of 0.05. The 30 predictors can be potentially reduced to at least 3 uncorrelated principal components demonstrating sufficient discrimination.
   • pc_1: T.Test.Statistic=-21.406, T.Test.PValue=0.000
   • pc_2: T.Test.Statistic=+4.080, T.Test.PValue=0.000
   • pc_3: T.Test.Statistic=+3.192, T.Test.PValue=0.015
   • pc_14: T.Test.Statistic=-2.299, T.Test.PValue=0.022
   • pc_17: T.Test.Statistic=+2.256, T.Test.PValue=0.024
   • pc_20: T.Test.Statistic=-2.001, T.Test.PValue=0.046

##################################
# Computing the t-test 
# statistic and p-values
# between the target variable
# and numeric predictor columns
##################################
breast_cancer_train_numeric_ttest_target = {}
breast_cancer_train_numeric = breast_cancer_train.iloc[:,1:]
breast_cancer_train_numeric_columns = breast_cancer_train.iloc[:,1:].columns
for numeric_column in breast_cancer_train_numeric_columns:
    group_B = breast_cancer_train[breast_cancer_train.loc[:,'diagnosis']=='B']
    group_M = breast_cancer_train[breast_cancer_train.loc[:,'diagnosis']=='M']
    breast_cancer_train_numeric_ttest_target['diagnosis_' + numeric_column] = stats.ttest_ind(
        group_B[numeric_column], 
        group_M[numeric_column], 
        equal_var=True)

##################################
# Formulating the pairwise ttest summary
# between the target variable
# and numeric predictor columns
##################################
breast_cancer_train_numeric_hypothesistesting_summary = breast_cancer_train_numeric.from_dict(breast_cancer_train_numeric_ttest_target, orient='index')
breast_cancer_train_numeric_hypothesistesting_summary.columns = ['T.Test.Statistic', 'T.Test.PValue']
display(breast_cancer_train_numeric_hypothesistesting_summary.sort_values(by=['T.Test.PValue'], ascending=True).head(30))

	T.Test.Statistic	T.Test.PValue
diagnosis_perimeter_worst	-23.391423	5.216127e-71
diagnosis_radius_worst	-23.228204	2.124527e-70
diagnosis_concave points_worst	-21.365587	2.304689e-63
diagnosis_concave points_mean	-21.258584	5.896498e-63
diagnosis_area_worst	-20.310881	2.507249e-59
diagnosis_perimeter_mean	-20.086310	1.830848e-58
diagnosis_radius_mean	-19.510552	3.031653e-56
diagnosis_area_mean	-17.991971	2.290509e-50
diagnosis_concavity_mean	-15.314435	5.174576e-40
diagnosis_concavity_worst	-13.368057	1.245191e-32
diagnosis_compactness_mean	-12.647550	5.808618e-30
diagnosis_compactness_worst	-12.079671	6.827871e-28
diagnosis_radius_se	-11.532905	6.238111e-26
diagnosis_perimeter_se	-11.234387	7.087958e-25
diagnosis_area_se	-10.375886	6.586298e-22
diagnosis_symmetry_worst	-8.312820	2.780206e-15
diagnosis_texture_worst	-7.911132	4.296038e-14
diagnosis_smoothness_worst	-7.080658	9.290923e-12
diagnosis_texture_mean	-6.682817	1.055204e-10
diagnosis_concave points_se	-6.679983	1.073250e-10
diagnosis_symmetry_mean	-6.315327	9.103085e-10
diagnosis_smoothness_mean	-6.087615	3.308230e-09
diagnosis_fractal_dimension_worst	-4.740955	3.218718e-06
diagnosis_compactness_se	-3.733659	2.236727e-04
diagnosis_concavity_se	-2.703321	7.235270e-03
diagnosis_smoothness_se	2.425051	1.586462e-02
diagnosis_fractal_dimension_mean	1.513439	1.311644e-01
diagnosis_texture_se	0.432444	6.657128e-01
diagnosis_symmetry_se	0.155224	8.767432e-01
diagnosis_fractal_dimension_se	-0.073082	9.417872e-01

##################################
# Exploring a feature extraction approach
# using Principal Component Analysis
# to address the high number of correlated predictors
# noted with high skewness and outlier ratio
##################################
# Standardizing predictors to address
# differences in scaling
##################################
scaler = StandardScaler()
breast_cancer_train_numeric_scaled = scaler.fit_transform(breast_cancer_train_numeric) 
breast_cancer_train_numeric_scaled = pd.DataFrame(breast_cancer_train_numeric_scaled,
                                                  columns=breast_cancer_train_numeric.columns,
                                                  index=breast_cancer_train_numeric.index)

##################################
# Conducting Principal Component Analysis
# on the standardized predictors
##################################
n_components = breast_cancer_train_numeric_scaled.shape[1]
pca = PCA(n_components=n_components, svd_solver='full', random_state=987654321)
breast_cancer_train_numeric_scaled_pcs = pca.fit_transform(breast_cancer_train_numeric_scaled)

##################################
# Consolidating the principal components
# into a dataframe and reattaching
# the diagnosis target column
##################################
pc_cols = [f'pc_{i+1}' for i in range(n_components)]
breast_cancer_train_numeric_scaled_pcs = pd.DataFrame(breast_cancer_train_numeric_scaled_pcs, columns=pc_cols, index=breast_cancer_train_numeric_scaled.index)
breast_cancer_train_pcs = pd.concat([breast_cancer_train[['diagnosis']].copy(), breast_cancer_train_numeric_scaled_pcs], axis=1)

##################################
# Consolidating the explained variance ratio
# for the principal components
##################################
explained_variance_ratio = pca.explained_variance_ratio_
explained_variance_ratio_summary = pd.DataFrame({
    'PC': pc_cols,
    'Explained_Variance_Ratio': explained_variance_ratio,
    'Cumulative_Explained_Variance': np.cumsum(explained_variance_ratio)
}).set_index('PC')
display(explained_variance_ratio_summary)

	Explained_Variance_Ratio	Cumulative_Explained_Variance
PC
pc_1	0.426228	0.426228
pc_2	0.189411	0.615639
pc_3	0.101749	0.717388
pc_4	0.068995	0.786383
pc_5	0.058895	0.845278
pc_6	0.042254	0.887533
pc_7	0.022768	0.910300
pc_8	0.016543	0.926843
pc_9	0.014899	0.941743
pc_10	0.011865	0.953608
pc_11	0.010183	0.963790
pc_12	0.008323	0.972114
pc_13	0.007802	0.979915
pc_14	0.004232	0.984147
pc_15	0.002850	0.986997
pc_16	0.002469	0.989465
pc_17	0.001967	0.991433
pc_18	0.001811	0.993243
pc_19	0.001471	0.994714
pc_20	0.001133	0.995847
pc_21	0.000952	0.996800
pc_22	0.000891	0.997691
pc_23	0.000713	0.998404
pc_24	0.000599	0.999002
pc_25	0.000480	0.999482
pc_26	0.000242	0.999724
pc_27	0.000203	0.999927
pc_28	0.000044	0.999972
pc_29	0.000024	0.999996
pc_30	0.000004	1.000000

##################################
# Computing the t-test 
# statistic and p-values
# between the target variable
# and principal component predictor columns
##################################
breast_cancer_train_pcs_ttest_target = {}
breast_cancer_train_pcs_numeric = breast_cancer_train_pcs.iloc[:,1:]
breast_cancer_train_pcs_numeric_columns = breast_cancer_train_pcs.iloc[:,1:].columns
for numeric_column in breast_cancer_train_pcs_numeric_columns:
    group_B = breast_cancer_train_pcs[breast_cancer_train_pcs.loc[:,'diagnosis']=='B']
    group_M = breast_cancer_train_pcs[breast_cancer_train_pcs.loc[:,'diagnosis']=='M']
    breast_cancer_train_pcs_ttest_target['diagnosis_' + numeric_column] = stats.ttest_ind(
        group_B[numeric_column], 
        group_M[numeric_column], 
        equal_var=True)

##################################
# Formulating the pairwise ttest summary
# between the target variable
# and principal component predictor columns
##################################
breast_cancer_train_pcs_numeric_hypothesistesting_summary = breast_cancer_train_pcs_numeric.from_dict(breast_cancer_train_pcs_ttest_target, orient='index')
breast_cancer_train_pcs_numeric_hypothesistesting_summary.columns = ['T.Test.Statistic', 'T.Test.PValue']
display(breast_cancer_train_pcs_numeric_hypothesistesting_summary.sort_values(by=['T.Test.PValue'], ascending=True).head(30))

	T.Test.Statistic	T.Test.PValue
diagnosis_pc_1	-21.406124	1.614914e-63
diagnosis_pc_2	4.080724	5.686808e-05
diagnosis_pc_3	3.192160	1.553738e-03
diagnosis_pc_13	-2.299656	2.211727e-02
diagnosis_pc_17	2.256550	2.471705e-02
diagnosis_pc_20	-2.001077	4.623628e-02
diagnosis_pc_4	-1.925622	5.504581e-02
diagnosis_pc_5	-1.762550	7.893997e-02
diagnosis_pc_14	-1.532393	1.264228e-01
diagnosis_pc_15	1.358293	1.753365e-01
diagnosis_pc_19	1.279015	2.018272e-01
diagnosis_pc_30	1.130236	2.592313e-01
diagnosis_pc_24	1.123771	2.619603e-01
diagnosis_pc_12	-1.010027	3.132526e-01
diagnosis_pc_25	-0.976871	3.293781e-01
diagnosis_pc_8	-0.911846	3.625425e-01
diagnosis_pc_26	0.838271	4.025101e-01
diagnosis_pc_16	-0.650378	5.159193e-01
diagnosis_pc_7	-0.576641	5.645909e-01
diagnosis_pc_23	0.503616	6.148809e-01
diagnosis_pc_29	-0.494381	6.213796e-01
diagnosis_pc_28	0.373462	7.090540e-01
diagnosis_pc_11	-0.362203	7.174415e-01
diagnosis_pc_9	0.261159	7.941393e-01
diagnosis_pc_10	-0.225840	8.214716e-01
diagnosis_pc_18	-0.221574	8.247879e-01
diagnosis_pc_22	-0.201455	8.404724e-01
diagnosis_pc_6	0.155608	8.764409e-01
diagnosis_pc_21	-0.138978	8.895559e-01
diagnosis_pc_27	-0.105049	9.164037e-01

1.6. Premodelling Data Preparation

1.6.1 Preprocessed Data Description

1. Due to the considerable number of predictors noted with high skewness, outlier ratio and multicollinearity, standardization and PCA feature extraction were performed to address issues with distributional shape and pairwise correlation.
   • High skewness observed for 5 variables with Skewness>3 or Skewness<(-3).
     • area_se: Skewness = 6.562
     • concavity_se: Skewness = 5.648
     • fractal_dimension_se: Skewness = 4.280
     • perimeter_se: Skewness = 4.136
     • radius_se: Skewness = 3.775
   • Relatively high number of outliers observed for 7 numeric variables with Outlier.Ratio>0.05.
     • area_se: Outlier.Ratio = 0.110
     • radius_se: Outlier.Ratio = 0.075
     • perimeter_se: Outlier.Ratio = 0.075
     • smoothness_se: Outlier.Ratio = 0.059
     • compactness_se: Outlier.Ratio = 0.059
     • fractal_dimension_se: Outlier.Ratio = 0.056
     • symmetry_se: Outlier.Ratio = 0.050
   • High Pearson.Correlation values > 0.90 were noted for 4.60% (20/435) of the pairwise combinations of predictors:
     • radius_mean and perimeter_mean: Pearson.Correlation = 0.997
     • radius_worst and perimeter_worst: Pearson.Correlation = 0.993
     • perimeter_mean and area_mean: Pearson.Correlation = 0.985
     • radius_mean and area_mean: Pearson.Correlation = 0.984
     • radius_worst and area_worst: Pearson.Correlation = 0.982
     • perimeter_worst and area_worst: Pearson.Correlation = 0.978
     • perimeter_mean and perimeter_worst: Pearson.Correlation = 0.972
     • perimeter_mean and radius_worst: Pearson.Correlation = 0.972
     • radius_mean and radius_worst: Pearson.Correlation = 0.971
     • radius_se and perimeter_se: Pearson.Correlation = 0.971
     • radius_mean and perimeter_worst: Pearson.Correlation = 0.967
     • area_mean and area_worst: Pearson.Correlation = 0.964
     • area_mean and radius_worst: Pearson.Correlation = 0.958
     • area_mean and perimeter_worst: Pearson.Correlation = 0.955
     • perimeter_mean and area_worst: Pearson.Correlation = 0.951
     • radius_se and area_se: Pearson.Correlation = 0.948
     • radius_mean and area_worst: Pearson.Correlation = 0.948
     • perimeter_se and area_se: Pearson.Correlation = 0.942
     • texture_mean and texture_worst: Pearson.Correlation = 0.923
     • concave points_mean and concave points_worst: Pearson.Correlation = 0.911
     • concavity_mean and concave points_mean: Pearson.Correlation = 0.900
2. Based on the assessment of cumulative explained variance and discrimination power of the extracted principal components, the number of predictors can range from 3 to 10.
3. To enable diversity among predictors, 10 principal components were used for the downstream modeling process.
4. The preprocessed train dataset (final) is comprised of:
   • 319 rows (observations)
     • 200 diagnosis=B: 62.69%
     • 119 diagnosis=M: 37.30%
   • 11 columns (variables)
     • 1/11 target (categorical)
       • diagnosis
     • 10/11 predictor (numeric)
       • pc_1
       • pc_2
       • pc_3
       • pc_4
       • pc_5
       • pc_6
       • pc_7
       • pc_8
       • pc_9
       • pc_10

1.6.2 Preprocessing Pipeline Development

1. A preprocessing pipeline was formulated and applied to the train data (final), validation data and test data with the following actions:
   • Applied standardization to address difference in scales among the predictors
   • Performed data extraction using Principal Component Analysis of the scaled predictors
   • Filtered the predictors to the top 10 principal components

##################################
# Formulating a preprocessing pipeline
# that performs standardization,
# performs feature extraction using PCA, and
# filtering the first 10 principal components as predictors
##################################
def preprocess_dataset(train_df: pd.DataFrame, 
                       evaluation_df: pd.DataFrame, 
                       n_components: int = 10, 
                       random_state: int = 987654321) -> pd.DataFrame:  
    # Splitting the target and predictor columns
    target_col = train_df.columns[0]
    X_train = train_df.iloc[:, 1:]
    y_train = train_df.iloc[:, 0]
    X_test = evaluation_df.iloc[:, 1:]
    y_test = evaluation_df.iloc[:, 0]

    # Fitting StandardScaler on training data and transforming both training and evaluation data
    scaler = StandardScaler()
    X_train_scaled = scaler.fit_transform(X_train)
    X_test_scaled = scaler.transform(X_test)

    # Fitting PCA on training data on training data and transforming both training and evaluation data
    pca = PCA(n_components=min(n_components, X_train.shape[1]), random_state=random_state)
    X_train_pca = pca.fit_transform(X_train_scaled)
    X_test_pca = pca.transform(X_test_scaled)

    # Preparing the output DataFrame for the evaluation data
    pc_cols = [f'pc_{i+1}' for i in range(X_test_pca.shape[1])]
    scaled_pcatransformed_evaluation_df = pd.DataFrame(X_test_pca, columns=pc_cols, index=evaluation_df.index)

    # Add target column back as first column
    scaled_pcatransformed_evaluation_df.insert(0, target_col, y_test.values)

    # Printing variance explained for reference
    explained_var = np.cumsum(pca.explained_variance_ratio_)
    print(f"Explained Variance (First {n_components} PCs): {explained_var[-1]:.4f}")

    return scaled_pcatransformed_evaluation_df

##################################
# Applying the preprocessing pipeline
# to the train data
##################################
breast_cancer_preprocessed_train = preprocess_dataset(breast_cancer_train, breast_cancer_train, 10, 987654321)
X_preprocessed_train = breast_cancer_preprocessed_train.drop('diagnosis', axis = 1)
y_preprocessed_train = breast_cancer_preprocessed_train['diagnosis']
breast_cancer_preprocessed_train.to_csv(os.path.join("..", DATASETS_PREPROCESSED_TRAIN_PATH, "breast_cancer_preprocessed_train.csv"), index=False)
X_preprocessed_train.to_csv(os.path.join("..", DATASETS_PREPROCESSED_TRAIN_FEATURES_PATH, "X_preprocessed_train.csv"), index=False)
y_preprocessed_train.to_csv(os.path.join("..", DATASETS_PREPROCESSED_TRAIN_TARGET_PATH, "y_preprocessed_train.csv"), index=False)
print('Final Preprocessed Train Dataset Dimensions: ')
display(X_preprocessed_train.shape)
display(y_preprocessed_train.shape)
print('Final Preprocessed Train Target Variable Breakdown: ')
display(y_preprocessed_train.value_counts())
print('Final Preprocessed Train Target Variable Proportion: ')
display(y_preprocessed_train.value_counts(normalize = True))
breast_cancer_preprocessed_train.head()

Explained Variance (First 10 PCs): 0.9536
Final Preprocessed Train Dataset Dimensions: 

(319, 10)

(319,)

Final Preprocessed Train Target Variable Breakdown: 

diagnosis
B    200
M    119
Name: count, dtype: int64

Final Preprocessed Train Target Variable Proportion: 

diagnosis
B    0.626959
M    0.373041
Name: proportion, dtype: float64

	diagnosis	pc_1	pc_2	pc_3	pc_4	pc_5	pc_6	pc_7	pc_8	pc_9	pc_10
id
868826	M	3.729203	0.987215	3.540855	-2.064283	2.512443	1.936519	0.697969	0.871868	0.642028	-1.833888
8810703	M	12.079158	-6.698169	10.242397	-5.434204	3.701610	-1.501518	-4.413311	1.612258	1.425855	-1.835477
906878	B	-0.311673	0.128320	-1.056912	0.070388	-1.547663	0.331599	0.032196	-0.533350	0.293836	0.071285
911654	B	-0.474681	-0.957130	-0.280827	0.354585	-1.590079	-0.326743	-0.120392	-0.328281	-0.094953	-0.681747
903483	B	-3.766843	2.522881	1.905036	-0.056397	2.901107	-1.592187	-1.428407	0.134134	-0.774598	1.244052

##################################
# Applying the preprocessing pipeline
# to the validation data
##################################
breast_cancer_preprocessed_validation = preprocess_dataset(breast_cancer_validation, breast_cancer_validation, 10, 987654321)
X_preprocessed_validation = breast_cancer_preprocessed_validation.drop('diagnosis', axis = 1)
y_preprocessed_validation = breast_cancer_preprocessed_validation['diagnosis']
breast_cancer_preprocessed_validation.to_csv(os.path.join("..", DATASETS_PREPROCESSED_VALIDATION_PATH, "breast_cancer_preprocessed_validation.csv"), index=False)
X_preprocessed_validation.to_csv(os.path.join("..", DATASETS_PREPROCESSED_VALIDATION_FEATURES_PATH, "X_preprocessed_validation.csv"), index=False)
y_preprocessed_validation.to_csv(os.path.join("..", DATASETS_PREPROCESSED_VALIDATION_TARGET_PATH, "y_preprocessed_validation.csv"), index=False)
print('Final Preprocessed Validation Dataset Dimensions: ')
display(X_preprocessed_validation.shape)
display(y_preprocessed_validation.shape)
print('Final Preprocessed Validation Target Variable Breakdown: ')
display(y_preprocessed_validation.value_counts())
print('Final Preprocessed Validation Target Variable Proportion: ')
display(y_preprocessed_validation.value_counts(normalize = True))
breast_cancer_preprocessed_validation.head()

Explained Variance (First 10 PCs): 0.9658
Final Preprocessed Validation Dataset Dimensions: 

(107, 10)

(107,)

Final Preprocessed Validation Target Variable Breakdown: 

diagnosis
B    67
M    40
Name: count, dtype: int64

Final Preprocessed Validation Target Variable Proportion: 

diagnosis
B    0.626168
M    0.373832
Name: proportion, dtype: float64

	diagnosis	pc_1	pc_2	pc_3	pc_4	pc_5	pc_6	pc_7	pc_8	pc_9	pc_10
id
86355	M	13.035175	0.217957	2.105837	-0.636468	0.051561	-1.807528	-0.025319	0.404616	-0.454300	-1.499024
884948	M	7.208194	-2.366385	1.928770	0.199315	-0.748175	-1.513559	0.265762	-0.764441	0.007565	0.402246
915276	B	1.300337	8.300252	-0.043626	-1.908086	-1.499821	3.112851	-0.717757	0.515100	1.345107	-0.311807
858970	B	-2.512677	3.300052	1.674471	-2.190322	3.044812	-1.144982	0.227182	-0.581862	-0.484832	1.131556
898677	B	-2.418011	4.124441	2.878352	-0.155380	-0.288107	0.993082	-0.246339	1.222199	2.012470	-0.674194

##################################
# Applying the preprocessing pipeline
# to the test data
##################################
breast_cancer_preprocessed_test = preprocess_dataset(breast_cancer_test, breast_cancer_test, 10, 987654321)
X_preprocessed_test = breast_cancer_preprocessed_test.drop('diagnosis', axis = 1)
y_preprocessed_test = breast_cancer_preprocessed_test['diagnosis']
breast_cancer_preprocessed_test.to_csv(os.path.join("..", DATASETS_PREPROCESSED_TEST_PATH, "breast_cancer_preprocessed_test.csv"), index=False)
X_preprocessed_test.to_csv(os.path.join("..", DATASETS_PREPROCESSED_TEST_FEATURES_PATH, "X_preprocessed_test.csv"), index=False)
y_preprocessed_test.to_csv(os.path.join("..", DATASETS_PREPROCESSED_TEST_TARGET_PATH, "y_preprocessed_test.csv"), index=False)
print('Final Preprocessed Test Dataset Dimensions: ')
display(X_preprocessed_test.shape)
display(y_preprocessed_test.shape)
print('Final Preprocessed Test Target Variable Breakdown: ')
display(y_preprocessed_test.value_counts())
print('Final Preprocessed Test Target Variable Proportion: ')
display(y_preprocessed_test.value_counts(normalize = True))
breast_cancer_preprocessed_test.head()

Explained Variance (First 10 PCs): 0.9630
Final Preprocessed Test Dataset Dimensions: 

(143, 10)

(143,)

Final Preprocessed Test Target Variable Breakdown: 

diagnosis
B    90
M    53
Name: count, dtype: int64

Final Preprocessed Test Target Variable Proportion: 

diagnosis
B    0.629371
M    0.370629
Name: proportion, dtype: float64

	diagnosis	pc_1	pc_2	pc_3	pc_4	pc_5	pc_6	pc_7	pc_8	pc_9	pc_10
id
848406	M	0.203287	-1.498700	-0.973630	0.810168	0.458344	0.704048	0.268294	0.004397	0.546047	-0.413089
858981	B	-2.363761	3.025143	1.519950	0.627623	2.306716	1.541578	-0.148369	-0.031751	-0.071823	-1.159295
88350402	B	-2.316578	-1.273185	-0.261651	-1.193922	-0.203169	0.076551	0.687459	-0.161819	0.152953	-0.160444
9112594	B	-3.134608	-1.944446	-0.040192	2.182643	0.277373	0.231880	0.295401	-0.048081	-0.121538	0.193050
86409	B	4.139336	3.702540	2.670982	-0.154971	-5.773728	-1.251681	-1.610567	1.354328	-0.115852	-0.220181

##################################
# Defining a function to compute
# model performance
##################################
def model_performance_evaluation(y_true, y_pred):
    metric_name = ['Accuracy','Precision','Recall','F1','AUROC']
    metric_value = [accuracy_score(y_true, y_pred),
                   precision_score(y_true, y_pred),
                   recall_score(y_true, y_pred),
                   f1_score(y_true, y_pred),
                   roc_auc_score(y_true, y_pred)]    
    metric_summary = pd.DataFrame(zip(metric_name, metric_value),
                                  columns=['metric_name','metric_value']) 
    return(metric_summary)

1.7. Model Development and Validation

1.7.1 Random Forest

Random Forest is an ensemble learning method that builds multiple decision trees and combines their outputs to improve prediction accuracy and robustness in binary classification. Instead of relying on a single decision tree, it aggregates multiple trees, reducing overfitting and increasing generalizability. The algorithm works by training individual decision trees on bootstrapped samples of the dataset, where each tree is trained on a slightly different subset of data. Additionally, at each decision node, a random subset of features is considered for splitting, adding further diversity among the trees. The final classification is determined by majority voting across all trees. The main advantages of Random Forest include its resilience to overfitting, ability to handle high-dimensional data, and robustness against noisy data. However, it has limitations, such as higher computational cost due to multiple trees and reduced interpretability compared to a single decision tree. It can also struggle with highly imbalanced data unless additional techniques like class weighting are applied.

1. The random forest model from the sklearn.ensemble Python library API was implemented.
2. The model contains 4 hyperparameters for tuning:
   • criterion = function to measure the quality of a split made to vary between gini and entropy
   • max_depth = maximum depth of the tree made to vary between 3 and 6
   • min_samples_leaf = minimum number of samples required to be at a leaf node made to vary between 5 and 10
   • max_features = number of features to consider when looking for the best split made to vary between 7 and 9
3. A special hyperparameter (class_weight = balanced) was fixed to address the minimal 1.7:1 class imbalance observed between the B and M diagnosis categories.
4. Hyperparameter tuning was conducted using the 5-cycle 5-fold cross-validation method with optimal model performance using the F1 score determined for:
   • criterion = entropy
   • max_depth = 5
   • min_samples_leaf = 9
   • max_features = 5
5. The apparent model performance of the optimal model is summarized as follows:
   • Accuracy = 0.9749
   • Precision = 0.9743
   • Recall = 0.9579
   • F1 Score = 0.9661
   • AUROC = 0.9714
6. The independent validation model performance of the optimal model is summarized as follows:
   • Accuracy = 0.9345
   • Precision = 0.9714
   • Recall = 0.8500
   • F1 Score = 0.9066
   • AUROC = 0.9175
7. Sufficiently comparable apparent and independent validation model performance observed that might be indicative of the absence of excessive model overfitting.

##################################
# Defining the missing value imputation, scaling and PCA preprocessing parameters
##################################
scaling_pca_preprocessor = Pipeline([
    ('imputer', SimpleImputer(strategy='median')),
    ('scaler', StandardScaler()),           
    ('pca', PCA(n_components=10, random_state=987654321))  
])

##################################
# Defining the preprocessing and modeling pipeline parameters
##################################
bagged_rf_pipeline = Pipeline([
    ('scaling_pca_preprocessor', scaling_pca_preprocessor),
    ('bagged_rf_model', RandomForestClassifier(
        class_weight='balanced',
        random_state=987654321))
])

##################################
# Defining hyperparameter grid
##################################
bagged_rf_hyperparameter_grid = {
    'bagged_rf_model__criterion': ['gini', 'entropy'],
    'bagged_rf_model__max_depth': [3, 5],
    'bagged_rf_model__min_samples_leaf': [5, 10],
    'bagged_rf_model__max_features': [7, 9]
}

##################################
# Defining the cross-validation strategy (5-cycle 5-fold CV)
##################################
cv_strategy = RepeatedStratifiedKFold(n_splits=5, 
                                      n_repeats=5, 
                                      random_state=987654321)

##################################
# Performing Grid Search with cross-validation
##################################
bagged_rf_grid_search = GridSearchCV(
    estimator=bagged_rf_pipeline,
    param_grid=bagged_rf_hyperparameter_grid,
    scoring='f1',
    cv=cv_strategy,
    n_jobs=-1,
    verbose=1
)

##################################
# Encoding the response variables
# for model training and validation
##################################
y_train_encoded = y_train.map({'B': 0, 'M': 1})
y_validation_encoded = y_validation.map({'B': 0, 'M': 1})

##################################
# Fitting GridSearchCV
##################################
bagged_rf_grid_search.fit(X_train, y_train_encoded)

Fitting 25 folds for each of 16 candidates, totalling 400 fits

GridSearchCV(cv=RepeatedStratifiedKFold(n_repeats=5, n_splits=5, random_state=987654321),
             estimator=Pipeline(steps=[('scaling_pca_preprocessor',
                                        Pipeline(steps=[('imputer',
                                                         SimpleImputer(strategy='median')),
                                                        ('scaler',
                                                         StandardScaler()),
                                                        ('pca',
                                                         PCA(n_components=10,
                                                             random_state=987654321))])),
                                       ('bagged_rf_model',
                                        RandomForestClassifier(class_weight='balanced',
                                                               random_state=987654321))]),
             n_jobs=-1,
             param_grid={'bagged_rf_model__criterion': ['gini', 'entropy'],
                         'bagged_rf_model__max_depth': [3, 5],
                         'bagged_rf_model__max_features': [7, 9],
                         'bagged_rf_model__min_samples_leaf': [5, 10]},
             scoring='f1', verbose=1)

In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook.
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##################################
# Identifying the best model
##################################
bagged_rf_optimal = bagged_rf_grid_search.best_estimator_

##################################
# Evaluating the F1 scores
# on the training, cross-validation, and validation data
##################################
bagged_rf_optimal_f1_cv = bagged_rf_grid_search.best_score_
bagged_rf_optimal_f1_train = f1_score(y_train_encoded, bagged_rf_optimal.predict(X_train))
bagged_rf_optimal_f1_validation = f1_score(y_validation_encoded, bagged_rf_optimal.predict(X_validation))

##################################
# Identifying the optimal model
##################################
print('Best Bagged Model - Random Forest: ')
print(f"Best Random Forest Hyperparameters: {bagged_rf_grid_search.best_params_}")

Best Bagged Model - Random Forest: 
Best Random Forest Hyperparameters: {'bagged_rf_model__criterion': 'entropy', 'bagged_rf_model__max_depth': 5, 'bagged_rf_model__max_features': 9, 'bagged_rf_model__min_samples_leaf': 5}

##################################
# Summarizing the F1 score results
# and classification metrics
# on the training and cross-validated data
# to assess overfitting optimism
##################################
print(f"F1 Score on Cross-Validated Data: {bagged_rf_optimal_f1_cv:.4f}")
print(f"F1 Score on Training Data: {bagged_rf_optimal_f1_train:.4f}")
print("\nClassification Report on Train Data:\n", classification_report(y_train_encoded, bagged_rf_optimal.predict(X_train)))

F1 Score on Cross-Validated Data: 0.9121
F1 Score on Training Data: 0.9661

Classification Report on Train Data:
               precision    recall  f1-score   support

           0       0.98      0.98      0.98       200
           1       0.97      0.96      0.97       119

    accuracy                           0.97       319
   macro avg       0.97      0.97      0.97       319
weighted avg       0.97      0.97      0.97       319

##################################
# Formulating the raw and normalized
# confusion matrices
# from the train data
##################################
cm_raw = confusion_matrix(y_train_encoded, bagged_rf_optimal.predict(X_train))
cm_normalized = confusion_matrix(y_train_encoded, bagged_rf_optimal.predict(X_train), normalize='true')
fig, ax = plt.subplots(1, 2, figsize=(17, 8))
sns.heatmap(cm_raw, annot=True, fmt='d', cmap='Blues', ax=ax[0])
ax[0].set_title('Raw Confusion Matrix: Optimal Random Forest Train Performance', fontsize=11)
ax[0].set_xlabel('Predicted')
ax[0].set_ylabel('Actual')
sns.heatmap(cm_normalized, annot=True, fmt='.2f', cmap='Blues', ax=ax[1])
ax[1].set_title('Normalized Confusion Matrix: Optimal Random Forest Train Performance', fontsize=11)
ax[1].set_xlabel('Predicted')
ax[1].set_ylabel('Actual')
plt.tight_layout()
plt.show()

##################################
# Summarizing the F1 score results
# and classification metrics
# on the validation data
# to assess overfitting optimism
##################################
print(f"F1 Score on Validation Data: {bagged_rf_optimal_f1_validation:.4f}")
print("\nClassification Report on Validation Data:\n", classification_report(y_validation_encoded, bagged_rf_optimal.predict(X_validation)))

F1 Score on Validation Data: 0.9067

Classification Report on Validation Data:
               precision    recall  f1-score   support

           0       0.92      0.99      0.95        67
           1       0.97      0.85      0.91        40

    accuracy                           0.93       107
   macro avg       0.94      0.92      0.93       107
weighted avg       0.94      0.93      0.93       107

##################################
# Formulating the raw and normalized
# confusion matrices
# from the validation data
##################################
cm_raw = confusion_matrix(y_validation_encoded, bagged_rf_optimal.predict(X_validation))
cm_normalized = confusion_matrix(y_validation_encoded, bagged_rf_optimal.predict(X_validation), normalize='true')
fig, ax = plt.subplots(1, 2, figsize=(17, 8))
sns.heatmap(cm_raw, annot=True, fmt='d', cmap='Blues', ax=ax[0])
ax[0].set_title('Raw Confusion Matrix: Optimal Random Forest Validation Performance', fontsize=11)
ax[0].set_xlabel('Predicted')
ax[0].set_ylabel('Actual')
sns.heatmap(cm_normalized, annot=True, fmt='.2f', cmap='Blues', ax=ax[1])
ax[1].set_title('Normalized Confusion Matrix: Optimal Random Forest Validation Performance', fontsize=11)
ax[1].set_xlabel('Predicted')
ax[1].set_ylabel('Actual')
plt.tight_layout()
plt.show()

##################################
# Gathering the model evaluation metrics
# for the train data
##################################
bagged_rf_optimal_train = model_performance_evaluation(y_train_encoded, bagged_rf_optimal.predict(X_train))
bagged_rf_optimal_train['model'] = ['bagged_rf_optimal'] * 5
bagged_rf_optimal_train['set'] = ['train'] * 5
print('Optimal Random Forest Train Performance Metrics: ')
display(bagged_rf_optimal_train)

Optimal Random Forest Train Performance Metrics: 

	metric_name	metric_value	model	set
0	Accuracy	0.974922	bagged_rf_optimal	train
1	Precision	0.974359	bagged_rf_optimal	train
2	Recall	0.957983	bagged_rf_optimal	train
3	F1	0.966102	bagged_rf_optimal	train
4	AUROC	0.971492	bagged_rf_optimal	train

##################################
# Gathering the model evaluation metrics
# for the validation data
##################################
bagged_rf_optimal_validation = model_performance_evaluation(y_validation_encoded, bagged_rf_optimal.predict(X_validation))
bagged_rf_optimal_validation['model'] = ['bagged_rf_optimal'] * 5
bagged_rf_optimal_validation['set'] = ['validation'] * 5
print('Optimal Random Forest Validation Performance Metrics: ')
display(bagged_rf_optimal_validation)

Optimal Random Forest Validation Performance Metrics: 

	metric_name	metric_value	model	set
0	Accuracy	0.934579	bagged_rf_optimal	validation
1	Precision	0.971429	bagged_rf_optimal	validation
2	Recall	0.850000	bagged_rf_optimal	validation
3	F1	0.906667	bagged_rf_optimal	validation
4	AUROC	0.917537	bagged_rf_optimal	validation

##################################
# Saving the best individual model
# developed from the train data
################################## 
joblib.dump(bagged_rf_optimal, 
            os.path.join("..", MODELS_PATH, "bagged_model_random_forest_optimal.pkl"))

['..\\models\\bagged_model_random_forest_optimal.pkl']

1.7.2 AdaBoost

AdaBoost (Adaptive Boosting) is a boosting technique that combines multiple weak learners — typically decision stumps (shallow trees) — to form a strong classifier. It works by iteratively training weak models, assigning higher weights to misclassified instances so that subsequent models focus on difficult cases. At each iteration, a new weak model is trained, and its predictions are combined using a weighted voting mechanism. This process continues until a stopping criterion is met, such as a predefined number of iterations or performance threshold. AdaBoost is advantageous because it improves accuracy without overfitting if regularized properly. It performs well with clean data and can transform weak classifiers into strong ones. However, it is sensitive to noisy data and outliers, as misclassified points receive higher importance, leading to potential overfitting. Additionally, training can be slow for large datasets, and performance depends on the choice of base learner, typically decision trees.

1. The adaboost model from the sklearn.ensemble Python library API was implemented.
2. The model contains 3 hyperparameters for tuning:
   • estimator_max_depth = maximum depth of the tree made to vary between 1 and 2
   • learning_rate = weight applied to each classifier at each boosting iteration made to vary between 0.01 and 0.10
   • n_estimators = maximum number of estimators at which boosting is terminated made to vary between 50 and 100
3. No any hyperparameter was defined in the model address the minimal 1.7:1 class imbalance observed between the B and M diagnosis categories.
4. Hyperparameter tuning was conducted using the 5-cycle 5-fold cross-validation method with optimal model performance using the F1 score determined for:
   • estimator_max_depth = 2
   • learning_rate = 0.10
   • n_estimators = 100
5. The apparent model performance of the optimal model is summarized as follows:
   • Accuracy = 0.9937
   • Precision = 1.0000
   • Recall = 0.9831
   • F1 Score = 0.9915
   • AUROC = 0.9915
6. The independent validation model performance of the optimal model is summarized as follows:
   • Accuracy = 0.9439
   • Precision = 0.9722
   • Recall = 0.8750
   • F1 Score = 0.9210
   • AUROC = 0.9300
7. Sufficiently comparable apparent and independent validation model performance observed that might be indicative of the absence of excessive model overfitting.

##################################
# Defining the missing value imputation, scaling and PCA preprocessing parameters
##################################
scaling_pca_preprocessor = Pipeline([
    ('imputer', SimpleImputer(strategy='median')),
    ('scaler', StandardScaler()),           
    ('pca', PCA(n_components=10, random_state=987654321))  
])

##################################
# Defining the preprocessing and modeling pipeline parameters
##################################
boosted_ab_pipeline = Pipeline([
    ('scaling_pca_preprocessor', scaling_pca_preprocessor),
    ('boosted_ab_model', AdaBoostClassifier(estimator=DecisionTreeClassifier(random_state=987654321),
                                            random_state=987654321))
])

##################################
# Defining hyperparameter grid
##################################
boosted_ab_hyperparameter_grid = {
    'boosted_ab_model__learning_rate': [0.01, 0.10],  
    'boosted_ab_model__estimator__max_depth': [1, 2],
    'boosted_ab_model__n_estimators': [50, 100]
}

##################################
# Defining the cross-validation strategy (5-cycle 5-fold CV)
##################################
cv_strategy = RepeatedStratifiedKFold(n_splits=5, 
                                      n_repeats=5, 
                                      random_state=987654321)

##################################
# Performing Grid Search with cross-validation
##################################
boosted_ab_grid_search = GridSearchCV(
    estimator=boosted_ab_pipeline,
    param_grid=boosted_ab_hyperparameter_grid,
    scoring='f1',
    cv=cv_strategy,
    n_jobs=-1,
    verbose=1
)

##################################
# Encoding the response variables
# for model training and validation
##################################
y_train_encoded = y_train.map({'B': 0, 'M': 1})
y_validation_encoded = y_validation.map({'B': 0, 'M': 1})

##################################
# Fitting GridSearchCV
##################################
boosted_ab_grid_search.fit(X_train, y_train_encoded)

Fitting 25 folds for each of 8 candidates, totalling 200 fits

GridSearchCV(cv=RepeatedStratifiedKFold(n_repeats=5, n_splits=5, random_state=987654321),
             estimator=Pipeline(steps=[('scaling_pca_preprocessor',
                                        Pipeline(steps=[('imputer',
                                                         SimpleImputer(strategy='median')),
                                                        ('scaler',
                                                         StandardScaler()),
                                                        ('pca',
                                                         PCA(n_components=10,
                                                             random_state=987654321))])),
                                       ('boosted_ab_model',
                                        AdaBoostClassifier(estimator=DecisionTreeClassifier(random_state=987654321),
                                                           random_state=987654321))]),
             n_jobs=-1,
             param_grid={'boosted_ab_model__estimator__max_depth': [1, 2],
                         'boosted_ab_model__learning_rate': [0.01, 0.1],
                         'boosted_ab_model__n_estimators': [50, 100]},
             scoring='f1', verbose=1)

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##################################
# Identifying the best model
##################################
boosted_ab_optimal = boosted_ab_grid_search.best_estimator_

##################################
# Evaluating the F1 scores
# on the training, cross-validation, and validation data
##################################
boosted_ab_optimal_f1_cv = boosted_ab_grid_search.best_score_
boosted_ab_optimal_f1_train = f1_score(y_train_encoded, boosted_ab_optimal.predict(X_train))
boosted_ab_optimal_f1_validation = f1_score(y_validation_encoded, boosted_ab_optimal.predict(X_validation))

##################################
# Identifying the optimal model
##################################
print('Best Boosted Model - AdaBoost: ')
print(f"Best AdaBoost Hyperparameters: {boosted_ab_grid_search.best_params_}")

Best Boosted Model - AdaBoost: 
Best AdaBoost Hyperparameters: {'boosted_ab_model__estimator__max_depth': 2, 'boosted_ab_model__learning_rate': 0.1, 'boosted_ab_model__n_estimators': 100}

##################################
# Summarizing the F1 score results
# and classification metrics
# on the training and cross-validated data
# to assess overfitting optimism
##################################
print(f"F1 Score on Cross-Validated Data: {boosted_ab_optimal_f1_cv:.4f}")
print(f"F1 Score on Training Data: {boosted_ab_optimal_f1_train:.4f}")
print("\nClassification Report on Train Data:\n", classification_report(y_train_encoded, boosted_ab_optimal.predict(X_train)))

F1 Score on Cross-Validated Data: 0.9280
F1 Score on Training Data: 0.9915

Classification Report on Train Data:
               precision    recall  f1-score   support

           0       0.99      1.00      1.00       200
           1       1.00      0.98      0.99       119

    accuracy                           0.99       319
   macro avg       1.00      0.99      0.99       319
weighted avg       0.99      0.99      0.99       319

##################################
# Formulating the raw and normalized
# confusion matrices
# from the train data
##################################
cm_raw = confusion_matrix(y_train_encoded, boosted_ab_optimal.predict(X_train))
cm_normalized = confusion_matrix(y_train_encoded, boosted_ab_optimal.predict(X_train), normalize='true')
fig, ax = plt.subplots(1, 2, figsize=(17, 8))
sns.heatmap(cm_raw, annot=True, fmt='d', cmap='Blues', ax=ax[0])
ax[0].set_title('Raw Confusion Matrix: Optimal AdaBoost Train Performance', fontsize=11)
ax[0].set_xlabel('Predicted')
ax[0].set_ylabel('Actual')
sns.heatmap(cm_normalized, annot=True, fmt='.2f', cmap='Blues', ax=ax[1])
ax[1].set_title('Normalized Confusion Matrix: Optimal AdaBoost Train Performance', fontsize=11)
ax[1].set_xlabel('Predicted')
ax[1].set_ylabel('Actual')
plt.tight_layout()
plt.show()

##################################
# Summarizing the F1 score results
# and classification metrics
# on the validation data
# to assess overfitting optimism
##################################
print(f"F1 Score on Validation Data: {boosted_ab_optimal_f1_validation:.4f}")
print("\nClassification Report on Validation Data:\n", classification_report(y_validation_encoded, boosted_ab_optimal.predict(X_validation)))

F1 Score on Validation Data: 0.9211

Classification Report on Validation Data:
               precision    recall  f1-score   support

           0       0.93      0.99      0.96        67
           1       0.97      0.88      0.92        40

    accuracy                           0.94       107
   macro avg       0.95      0.93      0.94       107
weighted avg       0.95      0.94      0.94       107

##################################
# Formulating the raw and normalized
# confusion matrices
# from the validation data
##################################
cm_raw = confusion_matrix(y_validation_encoded, boosted_ab_optimal.predict(X_validation))
cm_normalized = confusion_matrix(y_validation_encoded, boosted_ab_optimal.predict(X_validation), normalize='true')
fig, ax = plt.subplots(1, 2, figsize=(17, 8))
sns.heatmap(cm_raw, annot=True, fmt='d', cmap='Blues', ax=ax[0])
ax[0].set_title('Raw Confusion Matrix: Optimal AdaBoost Validation Performance', fontsize=11)
ax[0].set_xlabel('Predicted')
ax[0].set_ylabel('Actual')
sns.heatmap(cm_normalized, annot=True, fmt='.2f', cmap='Blues', ax=ax[1])
ax[1].set_title('Normalized Confusion Matrix: Optimal AdaBoost Validation Performance', fontsize=11)
ax[1].set_xlabel('Predicted')
ax[1].set_ylabel('Actual')
plt.tight_layout()
plt.show()

##################################
# Gathering the model evaluation metrics
# for the train data
##################################
boosted_ab_optimal_train = model_performance_evaluation(y_train_encoded, boosted_ab_optimal.predict(X_train))
boosted_ab_optimal_train['model'] = ['boosted_ab_optimal'] * 5
boosted_ab_optimal_train['set'] = ['train'] * 5
print('Optimal AdaBoost Train Performance Metrics: ')
display(boosted_ab_optimal_train)

Optimal AdaBoost Train Performance Metrics: 

	metric_name	metric_value	model	set
0	Accuracy	0.993730	boosted_ab_optimal	train
1	Precision	1.000000	boosted_ab_optimal	train
2	Recall	0.983193	boosted_ab_optimal	train
3	F1	0.991525	boosted_ab_optimal	train
4	AUROC	0.991597	boosted_ab_optimal	train

##################################
# Gathering the model evaluation metrics
# for the validation data
##################################
boosted_ab_optimal_validation = model_performance_evaluation(y_validation_encoded, boosted_ab_optimal.predict(X_validation))
boosted_ab_optimal_validation['model'] = ['boosted_ab_optimal'] * 5
boosted_ab_optimal_validation['set'] = ['validation'] * 5
print('Optimal AdaBoost Validation Performance Metrics: ')
display(boosted_ab_optimal_validation)

Optimal AdaBoost Validation Performance Metrics: 

	metric_name	metric_value	model	set
0	Accuracy	0.943925	boosted_ab_optimal	validation
1	Precision	0.972222	boosted_ab_optimal	validation
2	Recall	0.875000	boosted_ab_optimal	validation
3	F1	0.921053	boosted_ab_optimal	validation
4	AUROC	0.930037	boosted_ab_optimal	validation

##################################
# Saving the best individual model
# developed from the train data
################################## 
joblib.dump(boosted_ab_optimal, 
            os.path.join("..", MODELS_PATH, "boosted_model_adaboost_optimal.pkl"))

['..\\models\\boosted_model_adaboost_optimal.pkl']

1.7.3 Gradient Boosting

Gradient Boosting builds an ensemble of decision trees sequentially, where each new tree corrects the mistakes of the previous ones by optimizing a loss function. Unlike AdaBoost, which reweights misclassified instances, Gradient Boosting fits each new tree to the residual errors of the previous model, gradually improving predictions. This process continues until a stopping criterion, such as a set number of trees, is met. The key advantages of Gradient Boosting include its flexibility to model complex relationships and strong predictive performance, often outperforming bagging methods. It can handle both numeric and categorical data well. However, it is prone to overfitting if not carefully tuned, especially with deep trees and too many iterations. It is also computationally expensive due to sequential training, and hyperparameter tuning (e.g., learning rate, number of trees, tree depth) can be challenging and time-consuming.

1. The gradient boosting model from the sklearn.ensemble Python library API was implemented.
2. The model contains 4 hyperparameters for tuning:
   • learning_rate = shrinking proportion of the contribution from each tree made to vary between 0.01 and 0.10
   • max_depth = maximum depth of the tree made to vary between 3 and 6
   • min_samples_leaf = minimum number of samples required to be at a leaf node made to vary between 5 and 10
   • n_estimators = number of boosting stages to perform made to vary between 50 and 100
3. No any hyperparameter was defined in the model to address the minimal 1.7:1 class imbalance observed between the B and M diagnosis categories.
4. Hyperparameter tuning was conducted using the 5-cycle 5-fold cross-validation method with optimal model performance using the F1 score determined for:
   • learning_rate = 0.10
   • max_depth = 3
   • min_samples_leaf = 10
   • n_estimators = 100
5. The apparent model performance of the optimal model is summarized as follows:
   • Accuracy = 1.0000
   • Precision = 1.0000
   • Recall = 1.0000
   • F1 Score = 1.0000
   • AUROC = 1.0000
6. The independent validation model performance of the optimal model is summarized as follows:
   • Accuracy = 0.9345
   • Precision = 0.9714
   • Recall = 0.8500
   • F1 Score = 0.9066
   • AUROC = 0.9175
7. Sufficiently comparable apparent and independent validation model performance observed that might be indicative of the absence of excessive model overfitting.

##################################
# Defining the missing value imputation, scaling and PCA preprocessing parameters
##################################
scaling_pca_preprocessor = Pipeline([
    ('imputer', SimpleImputer(strategy='median')),
    ('scaler', StandardScaler()),           
    ('pca', PCA(n_components=10, random_state=987654321))  
])

##################################
# Defining the preprocessing and modeling pipeline parameters
##################################
boosted_gb_pipeline = Pipeline([
    ('scaling_pca_preprocessor', scaling_pca_preprocessor),
    ('boosted_gb_model', GradientBoostingClassifier(n_iter_no_change=10,
                                                    validation_fraction=0.1,
                                                    tol=1e-4,
                                                    random_state=987654321))
])

##################################
# Defining hyperparameter grid
##################################
boosted_gb_hyperparameter_grid = {
    'boosted_gb_model__learning_rate': [0.01, 0.10],
    'boosted_gb_model__max_depth': [3, 6], 
    'boosted_gb_model__min_samples_leaf': [5, 10],
    'boosted_gb_model__n_estimators': [50, 100] 
}

##################################
# Defining the cross-validation strategy (5-cycle 5-fold CV)
##################################
cv_strategy = RepeatedStratifiedKFold(n_splits=5, 
                                      n_repeats=5, 
                                      random_state=987654321)

##################################
# Performing Grid Search with cross-validation
##################################
boosted_gb_grid_search = GridSearchCV(
    estimator=boosted_gb_pipeline,
    param_grid=boosted_gb_hyperparameter_grid,
    scoring='f1',
    cv=cv_strategy,
    n_jobs=-1,
    verbose=1
)

##################################
# Encoding the response variables
# for model training and validation
##################################
y_train_encoded = y_train.map({'B': 0, 'M': 1})
y_validation_encoded = y_validation.map({'B': 0, 'M': 1})

##################################
# Fitting GridSearchCV
##################################
boosted_gb_grid_search.fit(X_train, y_train_encoded)

Fitting 25 folds for each of 16 candidates, totalling 400 fits

GridSearchCV(cv=RepeatedStratifiedKFold(n_repeats=5, n_splits=5, random_state=987654321),
             estimator=Pipeline(steps=[('scaling_pca_preprocessor',
                                        Pipeline(steps=[('imputer',
                                                         SimpleImputer(strategy='median')),
                                                        ('scaler',
                                                         StandardScaler()),
                                                        ('pca',
                                                         PCA(n_components=10,
                                                             random_state=987654321))])),
                                       ('boosted_gb_model',
                                        GradientBoostingClassifier(n_iter_no_change=10,
                                                                   random_state=987654321))]),
             n_jobs=-1,
             param_grid={'boosted_gb_model__learning_rate': [0.01, 0.1],
                         'boosted_gb_model__max_depth': [3, 6],
                         'boosted_gb_model__min_samples_leaf': [5, 10],
                         'boosted_gb_model__n_estimators': [50, 100]},
             scoring='f1', verbose=1)

In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook.
On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.

##################################
# Identifying the best model
##################################
boosted_gb_optimal = boosted_gb_grid_search.best_estimator_

##################################
# Evaluating the F1 scores
# on the training, cross-validation, and validation data
##################################
boosted_gb_optimal_f1_cv = boosted_gb_grid_search.best_score_
boosted_gb_optimal_f1_train = f1_score(y_train_encoded, boosted_gb_optimal.predict(X_train))
boosted_gb_optimal_f1_validation = f1_score(y_validation_encoded, boosted_gb_optimal.predict(X_validation))

##################################
# Identifying the optimal model
##################################
print('Best Boosted Model - Gradient Boosting: ')
print(f"Best Gradient Boosting Hyperparameters: {boosted_gb_grid_search.best_params_}")

Best Boosted Model - Gradient Boosting: 
Best Gradient Boosting Hyperparameters: {'boosted_gb_model__learning_rate': 0.1, 'boosted_gb_model__max_depth': 3, 'boosted_gb_model__min_samples_leaf': 10, 'boosted_gb_model__n_estimators': 100}

##################################
# Summarizing the F1 score results
# and classification metrics
# on the training and cross-validated data
# to assess overfitting optimism
##################################
print(f"F1 Score on Cross-Validated Data: {boosted_gb_optimal_f1_cv:.4f}")
print(f"F1 Score on Training Data: {boosted_gb_optimal_f1_train:.4f}")
print("\nClassification Report on Train Data:\n", classification_report(y_train_encoded, boosted_gb_optimal.predict(X_train)))

F1 Score on Cross-Validated Data: 0.9330
F1 Score on Training Data: 1.0000

Classification Report on Train Data:
               precision    recall  f1-score   support

           0       1.00      1.00      1.00       200
           1       1.00      1.00      1.00       119

    accuracy                           1.00       319
   macro avg       1.00      1.00      1.00       319
weighted avg       1.00      1.00      1.00       319

##################################
# Formulating the raw and normalized
# confusion matrices
# from the train data
##################################
cm_raw = confusion_matrix(y_train_encoded, boosted_gb_optimal.predict(X_train))
cm_normalized = confusion_matrix(y_train_encoded, boosted_gb_optimal.predict(X_train), normalize='true')
fig, ax = plt.subplots(1, 2, figsize=(17, 8))
sns.heatmap(cm_raw, annot=True, fmt='d', cmap='Blues', ax=ax[0])
ax[0].set_title('Raw Confusion Matrix: Optimal Gradient Boosting Train Performance', fontsize=11)
ax[0].set_xlabel('Predicted')
ax[0].set_ylabel('Actual')
sns.heatmap(cm_normalized, annot=True, fmt='.2f', cmap='Blues', ax=ax[1])
ax[1].set_title('Normalized Confusion Matrix: Optimal Gradient Boosting Train Performance', fontsize=11)
ax[1].set_xlabel('Predicted')
ax[1].set_ylabel('Actual')
plt.tight_layout()
plt.show()

##################################
# Summarizing the F1 score results
# and classification metrics
# on the validation data
# to assess overfitting optimism
##################################
print(f"F1 Score on Validation Data: {boosted_gb_optimal_f1_validation:.4f}")
print("\nClassification Report on Validation Data:\n", classification_report(y_validation_encoded, boosted_gb_optimal.predict(X_validation)))

F1 Score on Validation Data: 0.9067

Classification Report on Validation Data:
               precision    recall  f1-score   support

           0       0.92      0.99      0.95        67
           1       0.97      0.85      0.91        40

    accuracy                           0.93       107
   macro avg       0.94      0.92      0.93       107
weighted avg       0.94      0.93      0.93       107

##################################
# Formulating the raw and normalized
# confusion matrices
# from the validation data
##################################
cm_raw = confusion_matrix(y_validation_encoded, boosted_gb_optimal.predict(X_validation))
cm_normalized = confusion_matrix(y_validation_encoded, boosted_gb_optimal.predict(X_validation), normalize='true')
fig, ax = plt.subplots(1, 2, figsize=(17, 8))
sns.heatmap(cm_raw, annot=True, fmt='d', cmap='Blues', ax=ax[0])
ax[0].set_title('Raw Confusion Matrix: Optimal Gradient Boosting Validation Performance', fontsize=11)
ax[0].set_xlabel('Predicted')
ax[0].set_ylabel('Actual')
sns.heatmap(cm_normalized, annot=True, fmt='.2f', cmap='Blues', ax=ax[1])
ax[1].set_title('Normalized Confusion Matrix: Optimal Gradient Boosting Validation Performance', fontsize=11)
ax[1].set_xlabel('Predicted')
ax[1].set_ylabel('Actual')
plt.tight_layout()
plt.show()

##################################
# Gathering the model evaluation metrics
# for the train data
##################################
boosted_gb_optimal_train = model_performance_evaluation(y_train_encoded, boosted_gb_optimal.predict(X_train))
boosted_gb_optimal_train['model'] = ['boosted_gb_optimal'] * 5
boosted_gb_optimal_train['set'] = ['train'] * 5
print('Optimal Gradient Boosting Train Performance Metrics: ')
display(boosted_gb_optimal_train)

Optimal Gradient Boosting Train Performance Metrics: 

	metric_name	metric_value	model	set
0	Accuracy	1.0	boosted_gb_optimal	train
1	Precision	1.0	boosted_gb_optimal	train
2	Recall	1.0	boosted_gb_optimal	train
3	F1	1.0	boosted_gb_optimal	train
4	AUROC	1.0	boosted_gb_optimal	train

##################################
# Gathering the model evaluation metrics
# for the validation data
##################################
boosted_gb_optimal_validation = model_performance_evaluation(y_validation_encoded, boosted_gb_optimal.predict(X_validation))
boosted_gb_optimal_validation['model'] = ['boosted_gb_optimal'] * 5
boosted_gb_optimal_validation['set'] = ['validation'] * 5
print('Optimal Gradient Boosting Validation Performance Metrics: ')
display(boosted_gb_optimal_validation)

Optimal Gradient Boosting Validation Performance Metrics: 

	metric_name	metric_value	model	set
0	Accuracy	0.934579	boosted_gb_optimal	validation
1	Precision	0.971429	boosted_gb_optimal	validation
2	Recall	0.850000	boosted_gb_optimal	validation
3	F1	0.906667	boosted_gb_optimal	validation
4	AUROC	0.917537	boosted_gb_optimal	validation

##################################
# Saving the best individual model
# developed from the train data
################################## 
joblib.dump(boosted_gb_optimal, 
            os.path.join("..", MODELS_PATH, "boosted_model_gradient_boosting_optimal.pkl"))

['..\\models\\boosted_model_gradient_boosting_optimal.pkl']

1.7.4 XGBoost

XGBoost (Extreme Gradient Boosting) is an optimized version of Gradient Boosting that introduces additional regularization and computational efficiencies. It builds decision trees sequentially, with each new tree correcting the residual errors of the previous ones, but it incorporates advanced techniques such as shrinkage (learning rate), column subsampling, and L1/L2 regularization to prevent overfitting. Additionally, XGBoost employs parallelization, reducing training time significantly compared to standard Gradient Boosting. It is widely used in machine learning competitions due to its superior accuracy and efficiency. The key advantages include its ability to handle missing data, built-in regularization for better generalization, and fast training through parallelization. However, XGBoost requires careful hyperparameter tuning to achieve optimal performance, and the model can become overly complex, making interpretation difficult. It is also memory-intensive, especially for large datasets, and can be challenging to deploy efficiently in real-time applications.

1. The xgboost model from the xgboost Python library API was implemented.
2. The model contains 4 hyperparameters for tuning:
   • learning_rate = step size at which weights are updated during training made to vary between 0.01 and 0.10
   • max_depth = maximum depth of the tree made to vary between 3 and 6
   • gamma = minimum loss reduction required to make a further split in a tree made to vary between 0.10 and 0.20
   • n_estimators = number of boosting stages to perform made to vary between 50 and 100
3. A special hyperparameter (scale_pos_weight = 1.7) was fixed to address the minimal 1.7:1 class imbalance observed between the B and M diagnosis categories.
4. Hyperparameter tuning was conducted using the 5-cycle 5-fold cross-validation method with optimal model performance using the F1 score determined for:
   • learning_rate = 0.10
   • max_depth = 6
   • gamma 0.20
   • n_estimators = 100
5. The apparent model performance of the optimal model is summarized as follows:
   • Accuracy = 1.0000
   • Precision = 1.0000
   • Recall = 1.0000
   • F1 Score = 1.0000
   • AUROC = 1.0000
6. The independent validation model performance of the optimal model is summarized as follows:
   • Accuracy = 0.9439
   • Precision = 0.9722
   • Recall = 0.8750
   • F1 Score = 0.9210
   • AUROC = 0.9300
7. Sufficiently comparable apparent and independent validation model performance observed that might be indicative of the absence of excessive model overfitting.

##################################
# Defining the missing value imputation, scaling and PCA preprocessing parameters
##################################
scaling_pca_preprocessor = Pipeline([
    ('imputer', SimpleImputer(strategy='median')),
    ('scaler', StandardScaler()),           
    ('pca', PCA(n_components=10, random_state=987654321))  
])

##################################
# Defining the preprocessing and modeling pipeline parameters
##################################
boosted_xgb_pipeline = Pipeline([
    ('scaling_pca_preprocessor', scaling_pca_preprocessor),
    ('boosted_xgb_model', XGBClassifier(scale_pos_weight=1.7, 
                                        random_state=987654321,
                                        subsample=0.7,
                                        colsample_bytree=0.7,
                                        eval_metric='logloss'))
])

##################################
# Defining hyperparameter grid
##################################
boosted_xgb_hyperparameter_grid = {
    'boosted_xgb_model__learning_rate': [0.01, 0.10],
    'boosted_xgb_model__max_depth': [3, 6], 
    'boosted_xgb_model__gamma': [0.1, 0.2],
    'boosted_xgb_model__n_estimators': [50, 100]
}

##################################
# Defining the cross-validation strategy (5-cycle 5-fold CV)
##################################
cv_strategy = RepeatedStratifiedKFold(n_splits=5, 
                                      n_repeats=5, 
                                      random_state=987654321)

##################################
# Performing Grid Search with cross-validation
##################################
boosted_xgb_grid_search = GridSearchCV(
    estimator=boosted_xgb_pipeline,
    param_grid=boosted_xgb_hyperparameter_grid,
    scoring='f1',
    cv=cv_strategy,
    n_jobs=-1,
    verbose=1
)

##################################
# Encoding the response variables
# for model training and validation
##################################
y_train_encoded = y_train.map({'B': 0, 'M': 1})
y_validation_encoded = y_validation.map({'B': 0, 'M': 1})

##################################
# Fitting GridSearchCV
##################################
boosted_xgb_grid_search.fit(X_train, y_train_encoded)

Fitting 25 folds for each of 16 candidates, totalling 400 fits

GridSearchCV(cv=RepeatedStratifiedKFold(n_repeats=5, n_splits=5, random_state=987654321),
             estimator=Pipeline(steps=[('scaling_pca_preprocessor',
                                        Pipeline(steps=[('imputer',
                                                         SimpleImputer(strategy='median')),
                                                        ('scaler',
                                                         StandardScaler()),
                                                        ('pca',
                                                         PCA(n_components=10,
                                                             random_state=987654321))])),
                                       ('boosted_xgb_model',
                                        XGBClassifier(base_score=None,
                                                      booster=None,
                                                      c...
                                                      missing=nan,
                                                      monotone_constraints=None,
                                                      multi_strategy=None,
                                                      n_estimators=None,
                                                      n_jobs=None,
                                                      num_parallel_tree=None,
                                                      random_state=987654321, ...))]),
             n_jobs=-1,
             param_grid={'boosted_xgb_model__gamma': [0.1, 0.2],
                         'boosted_xgb_model__learning_rate': [0.01, 0.1],
                         'boosted_xgb_model__max_depth': [3, 6],
                         'boosted_xgb_model__n_estimators': [50, 100]},
             scoring='f1', verbose=1)

In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook.
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##################################
# Identifying the best model
##################################
boosted_xgb_optimal = boosted_xgb_grid_search.best_estimator_

##################################
# Evaluating the F1 scores
# on the training, cross-validation, and validation data
##################################
boosted_xgb_optimal_f1_cv = boosted_xgb_grid_search.best_score_
boosted_xgb_optimal_f1_train = f1_score(y_train_encoded, boosted_xgb_optimal.predict(X_train))
boosted_xgb_optimal_f1_validation = f1_score(y_validation_encoded, boosted_xgb_optimal.predict(X_validation))

##################################
# Identifying the optimal model
##################################
print('Best Boosted Model - XGBoost: ')
print(f"Best XGBoost Hyperparameters: {boosted_xgb_grid_search.best_params_}")

Best Boosted Model - XGBoost: 
Best XGBoost Hyperparameters: {'boosted_xgb_model__gamma': 0.2, 'boosted_xgb_model__learning_rate': 0.1, 'boosted_xgb_model__max_depth': 6, 'boosted_xgb_model__n_estimators': 100}

##################################
# Summarizing the F1 score results
# and classification metrics
# on the training and cross-validated data
# to assess overfitting optimism
##################################
print(f"F1 Score on Cross-Validated Data: {boosted_xgb_optimal_f1_cv:.4f}")
print(f"F1 Score on Training Data: {boosted_xgb_optimal_f1_train:.4f}")
print("\nClassification Report on Train Data:\n", classification_report(y_train_encoded, boosted_xgb_optimal.predict(X_train)))

F1 Score on Cross-Validated Data: 0.9461
F1 Score on Training Data: 1.0000

Classification Report on Train Data:
               precision    recall  f1-score   support

           0       1.00      1.00      1.00       200
           1       1.00      1.00      1.00       119

    accuracy                           1.00       319
   macro avg       1.00      1.00      1.00       319
weighted avg       1.00      1.00      1.00       319

##################################
# Formulating the raw and normalized
# confusion matrices
# from the train data
##################################
cm_raw = confusion_matrix(y_train_encoded, boosted_xgb_optimal.predict(X_train))
cm_normalized = confusion_matrix(y_train_encoded, boosted_xgb_optimal.predict(X_train), normalize='true')
fig, ax = plt.subplots(1, 2, figsize=(17, 8))
sns.heatmap(cm_raw, annot=True, fmt='d', cmap='Blues', ax=ax[0])
ax[0].set_title('Raw Confusion Matrix: Optimal XGBoost Train Performance', fontsize=11)
ax[0].set_xlabel('Predicted')
ax[0].set_ylabel('Actual')
sns.heatmap(cm_normalized, annot=True, fmt='.2f', cmap='Blues', ax=ax[1])
ax[1].set_title('Normalized Confusion Matrix: Optimal XGBoost Train Performance', fontsize=11)
ax[1].set_xlabel('Predicted')
ax[1].set_ylabel('Actual')
plt.tight_layout()
plt.show()

##################################
# Summarizing the F1 score results
# and classification metrics
# on the validation data
# to assess overfitting optimism
##################################
print(f"F1 Score on Validation Data: {boosted_xgb_optimal_f1_validation:.4f}")
print("\nClassification Report on Validation Data:\n", classification_report(y_validation_encoded, boosted_xgb_optimal.predict(X_validation)))

F1 Score on Validation Data: 0.9211

Classification Report on Validation Data:
               precision    recall  f1-score   support

           0       0.93      0.99      0.96        67
           1       0.97      0.88      0.92        40

    accuracy                           0.94       107
   macro avg       0.95      0.93      0.94       107
weighted avg       0.95      0.94      0.94       107

##################################
# Formulating the raw and normalized
# confusion matrices
# from the validation data
##################################
cm_raw = confusion_matrix(y_validation_encoded, boosted_xgb_optimal.predict(X_validation))
cm_normalized = confusion_matrix(y_validation_encoded, boosted_xgb_optimal.predict(X_validation), normalize='true')
fig, ax = plt.subplots(1, 2, figsize=(17, 8))
sns.heatmap(cm_raw, annot=True, fmt='d', cmap='Blues', ax=ax[0])
ax[0].set_title('Raw Confusion Matrix: Optimal XGBoost Validation Performance', fontsize=11)
ax[0].set_xlabel('Predicted')
ax[0].set_ylabel('Actual')
sns.heatmap(cm_normalized, annot=True, fmt='.2f', cmap='Blues', ax=ax[1])
ax[1].set_title('Normalized Confusion Matrix: Optimal XGBoost Validation Performance', fontsize=11)
ax[1].set_xlabel('Predicted')
ax[1].set_ylabel('Actual')
plt.tight_layout()
plt.show()

##################################
# Gathering the model evaluation metrics
# for the train data
##################################
boosted_xgb_optimal_train = model_performance_evaluation(y_train_encoded, boosted_xgb_optimal.predict(X_train))
boosted_xgb_optimal_train['model'] = ['boosted_xgb_optimal'] * 5
boosted_xgb_optimal_train['set'] = ['train'] * 5
print('Optimal XGBoost Train Performance Metrics: ')
display(boosted_xgb_optimal_train)

Optimal XGBoost Train Performance Metrics: 

	metric_name	metric_value	model	set
0	Accuracy	1.0	boosted_xgb_optimal	train
1	Precision	1.0	boosted_xgb_optimal	train
2	Recall	1.0	boosted_xgb_optimal	train
3	F1	1.0	boosted_xgb_optimal	train
4	AUROC	1.0	boosted_xgb_optimal	train

##################################
# Gathering the model evaluation metrics
# for the validation data
##################################
boosted_xgb_optimal_validation = model_performance_evaluation(y_validation_encoded, boosted_xgb_optimal.predict(X_validation))
boosted_xgb_optimal_validation['model'] = ['boosted_xgb_optimal'] * 5
boosted_xgb_optimal_validation['set'] = ['validation'] * 5
print('Optimal XGBoost Validation Performance Metrics: ')
display(boosted_xgb_optimal_validation)

Optimal XGBoost Validation Performance Metrics: 

	metric_name	metric_value	model	set
0	Accuracy	0.943925	boosted_xgb_optimal	validation
1	Precision	0.972222	boosted_xgb_optimal	validation
2	Recall	0.875000	boosted_xgb_optimal	validation
3	F1	0.921053	boosted_xgb_optimal	validation
4	AUROC	0.930037	boosted_xgb_optimal	validation

##################################
# Saving the best individual model
# developed from the train data
################################## 
joblib.dump(boosted_xgb_optimal, 
            os.path.join("..", MODELS_PATH, "boosted_model_xgboost_optimal.pkl"))

['..\\models\\boosted_model_xgboost_optimal.pkl']

1.7.5 Light GBM

Light GBM (Light Gradient Boosting Machine) is a variation of Gradient Boosting designed for efficiency and scalability. Unlike traditional boosting methods that grow trees level by level, LightGBM grows trees leaf-wise, choosing the most informative splits, leading to faster convergence. It also uses histogram-based binning to speed up computations. These optimizations allow LightGBM to train on large datasets efficiently while maintaining high accuracy. Its advantages include faster training speed, reduced memory usage, and strong predictive performance, particularly for large datasets with many features. However, LightGBM can overfit more easily than XGBoost if not properly tuned, and it may not perform as well on small datasets. Additionally, its handling of categorical variables requires careful preprocessing, and the leaf-wise tree growth can sometimes lead to instability if not controlled properly.

1. The light gbm model from the lightgbm Python library API was implemented.
2. The model contains 4 hyperparameters for tuning:
   • learning_rate = step size at which weights are updated during training made to vary between 0.01 and 0.10
   • min_child_samples = minimum number of data needed in a child 3 and 6
   • num_leaves = maximum tree leaves for base learners made to vary between 8 and 16
   • n_estimators = number of boosted trees to fit made to vary between 50 and 100
3. A special hyperparameter (scale_pos_weight = 1.7) was fixed to address the minimal 1.7:1 class imbalance observed between the B and M diagnosis categories.
4. Hyperparameter tuning was conducted using the 5-cycle 5-fold cross-validation method with optimal model performance using the F1 score determined for:
   • learning_rate = 0.10
   • min_child_samples = 6
   • num_leaves 16
   • n_estimators = 50
5. The apparent model performance of the optimal model is summarized as follows:
   • Accuracy = 1.0000
   • Precision = 1.0000
   • Recall = 1.0000
   • F1 Score = 1.0000
   • AUROC = 1.0000
6. The independent validation model performance of the optimal model is summarized as follows:
   • Accuracy = 0.9532
   • Precision = 0.9729
   • Recall = 0.9000
   • F1 Score = 0.9350
   • AUROC = 0.9425
7. Sufficiently comparable apparent and independent validation model performance observed that might be indicative of the absence of excessive model overfitting.

##################################
# Defining the missing value imputation, scaling and PCA preprocessing parameters
##################################
scaling_pca_preprocessor = Pipeline([
    ('imputer', SimpleImputer(strategy='median')),
    ('scaler', StandardScaler()),           
    ('pca', PCA(n_components=10, random_state=987654321))  
])

##################################
# Defining the preprocessing and modeling pipeline parameters
##################################
boosted_lgbm_pipeline = Pipeline([
    ('scaling_pca_preprocessor', scaling_pca_preprocessor),
    ('boosted_lgbm_model', LGBMClassifier(scale_pos_weight=1.7, 
                                          random_state=987654321,
                                          max_depth=-1,
                                          feature_fraction =0.7,
                                          bagging_fraction=0.7,
                                          verbose=-1))
])

##################################
# Defining hyperparameter grid
##################################
boosted_lgbm_hyperparameter_grid = {
    'boosted_lgbm_model__learning_rate': [0.01, 0.10],
    'boosted_lgbm_model__min_child_samples': [3, 6], 
    'boosted_lgbm_model__num_leaves': [8, 16],
    'boosted_lgbm_model__n_estimators': [50, 100] 
}

##################################
# Defining the cross-validation strategy (5-cycle 5-fold CV)
##################################
cv_strategy = RepeatedStratifiedKFold(n_splits=5, 
                                      n_repeats=5, 
                                      random_state=987654321)

##################################
# Performing Grid Search with cross-validation
##################################
boosted_lgbm_grid_search = GridSearchCV(
    estimator=boosted_lgbm_pipeline,
    param_grid=boosted_lgbm_hyperparameter_grid,
    scoring='f1',
    cv=cv_strategy,
    n_jobs=-1,
    verbose=1
)

##################################
# Encoding the response variables
# for model training and validation
##################################
y_train_encoded = y_train.map({'B': 0, 'M': 1})
y_validation_encoded = y_validation.map({'B': 0, 'M': 1})

##################################
# Fitting GridSearchCV
##################################
boosted_lgbm_grid_search.fit(X_train, y_train_encoded)

Fitting 25 folds for each of 16 candidates, totalling 400 fits

GridSearchCV(cv=RepeatedStratifiedKFold(n_repeats=5, n_splits=5, random_state=987654321),
             estimator=Pipeline(steps=[('scaling_pca_preprocessor',
                                        Pipeline(steps=[('imputer',
                                                         SimpleImputer(strategy='median')),
                                                        ('scaler',
                                                         StandardScaler()),
                                                        ('pca',
                                                         PCA(n_components=10,
                                                             random_state=987654321))])),
                                       ('boosted_lgbm_model',
                                        LGBMClassifier(bagging_fraction=0.7,
                                                       feature_fraction=0.7,
                                                       random_state=987654321,
                                                       scale_pos_weight=1.7,
                                                       verbose=-1))]),
             n_jobs=-1,
             param_grid={'boosted_lgbm_model__learning_rate': [0.01, 0.1],
                         'boosted_lgbm_model__min_child_samples': [3, 6],
                         'boosted_lgbm_model__n_estimators': [50, 100],
                         'boosted_lgbm_model__num_leaves': [8, 16]},
             scoring='f1', verbose=1)

In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook.
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##################################
# Identifying the best model
##################################
boosted_lgbm_optimal = boosted_lgbm_grid_search.best_estimator_

##################################
# Evaluating the F1 scores
# on the training, cross-validation, and validation data
##################################
boosted_lgbm_optimal_f1_cv = boosted_lgbm_grid_search.best_score_
boosted_lgbm_optimal_f1_train = f1_score(y_train_encoded, boosted_lgbm_optimal.predict(X_train))
boosted_lgbm_optimal_f1_validation = f1_score(y_validation_encoded, boosted_lgbm_optimal.predict(X_validation))

##################################
# Identifying the optimal model
##################################
print('Best Boosted Model - Light GBM: ')
print(f"Best Light GBM Hyperparameters: {boosted_lgbm_grid_search.best_params_}")

Best Boosted Model - Light GBM: 
Best Light GBM Hyperparameters: {'boosted_lgbm_model__learning_rate': 0.1, 'boosted_lgbm_model__min_child_samples': 6, 'boosted_lgbm_model__n_estimators': 50, 'boosted_lgbm_model__num_leaves': 16}

##################################
# Summarizing the F1 score results
# and classification metrics
# on the training and cross-validated data
# to assess overfitting optimism
##################################
print(f"F1 Score on Cross-Validated Data: {boosted_lgbm_optimal_f1_cv:.4f}")
print(f"F1 Score on Training Data: {boosted_lgbm_optimal_f1_train:.4f}")
print("\nClassification Report on Train Data:\n", classification_report(y_train_encoded, boosted_lgbm_optimal.predict(X_train)))

F1 Score on Cross-Validated Data: 0.9385
F1 Score on Training Data: 1.0000

Classification Report on Train Data:
               precision    recall  f1-score   support

           0       1.00      1.00      1.00       200
           1       1.00      1.00      1.00       119

    accuracy                           1.00       319
   macro avg       1.00      1.00      1.00       319
weighted avg       1.00      1.00      1.00       319

##################################
# Formulating the raw and normalized
# confusion matrices
# from the train data
##################################
cm_raw = confusion_matrix(y_train_encoded, boosted_lgbm_optimal.predict(X_train))
cm_normalized = confusion_matrix(y_train_encoded, boosted_lgbm_optimal.predict(X_train), normalize='true')
fig, ax = plt.subplots(1, 2, figsize=(17, 8))
sns.heatmap(cm_raw, annot=True, fmt='d', cmap='Blues', ax=ax[0])
ax[0].set_title('Raw Confusion Matrix: Optimal Light GBM Train Performance', fontsize=11)
ax[0].set_xlabel('Predicted')
ax[0].set_ylabel('Actual')
sns.heatmap(cm_normalized, annot=True, fmt='.2f', cmap='Blues', ax=ax[1])
ax[1].set_title('Normalized Confusion Matrix: Optimal Light GBM Train Performance', fontsize=11)
ax[1].set_xlabel('Predicted')
ax[1].set_ylabel('Actual')
plt.tight_layout()
plt.show()

##################################
# Summarizing the F1 score results
# and classification metrics
# on the validation data
# to assess overfitting optimism
##################################
print(f"F1 Score on Validation Data: {boosted_lgbm_optimal_f1_validation:.4f}")
print("\nClassification Report on Validation Data:\n", classification_report(y_validation_encoded, boosted_lgbm_optimal.predict(X_validation)))

F1 Score on Validation Data: 0.9351

Classification Report on Validation Data:
               precision    recall  f1-score   support

           0       0.94      0.99      0.96        67
           1       0.97      0.90      0.94        40

    accuracy                           0.95       107
   macro avg       0.96      0.94      0.95       107
weighted avg       0.95      0.95      0.95       107

##################################
# Formulating the raw and normalized
# confusion matrices
# from the validation data
##################################
cm_raw = confusion_matrix(y_validation_encoded, boosted_lgbm_optimal.predict(X_validation))
cm_normalized = confusion_matrix(y_validation_encoded, boosted_lgbm_optimal.predict(X_validation), normalize='true')
fig, ax = plt.subplots(1, 2, figsize=(17, 8))
sns.heatmap(cm_raw, annot=True, fmt='d', cmap='Blues', ax=ax[0])
ax[0].set_title('Raw Confusion Matrix: Optimal Light GBM Validation Performance', fontsize=11)
ax[0].set_xlabel('Predicted')
ax[0].set_ylabel('Actual')
sns.heatmap(cm_normalized, annot=True, fmt='.2f', cmap='Blues', ax=ax[1])
ax[1].set_title('Normalized Confusion Matrix: Optimal Light GBM Validation Performance', fontsize=11)
ax[1].set_xlabel('Predicted')
ax[1].set_ylabel('Actual')
plt.tight_layout()
plt.show()

##################################
# Gathering the model evaluation metrics
# for the train data
##################################
boosted_lgbm_optimal_train = model_performance_evaluation(y_train_encoded, boosted_lgbm_optimal.predict(X_train))
boosted_lgbm_optimal_train['model'] = ['boosted_lgbm_optimal'] * 5
boosted_lgbm_optimal_train['set'] = ['train'] * 5
print('Optimal Light GBM Train Performance Metrics: ')
display(boosted_lgbm_optimal_train)

Optimal Light GBM Train Performance Metrics: 

	metric_name	metric_value	model	set
0	Accuracy	1.0	boosted_lgbm_optimal	train
1	Precision	1.0	boosted_lgbm_optimal	train
2	Recall	1.0	boosted_lgbm_optimal	train
3	F1	1.0	boosted_lgbm_optimal	train
4	AUROC	1.0	boosted_lgbm_optimal	train

##################################
# Gathering the model evaluation metrics
# for the validation data
##################################
boosted_lgbm_optimal_validation = model_performance_evaluation(y_validation_encoded, boosted_lgbm_optimal.predict(X_validation))
boosted_lgbm_optimal_validation['model'] = ['boosted_lgbm_optimal'] * 5
boosted_lgbm_optimal_validation['set'] = ['validation'] * 5
print('Optimal Light GBM Validation Performance Metrics: ')
display(boosted_lgbm_optimal_validation)

Optimal Light GBM Validation Performance Metrics: 

	metric_name	metric_value	model	set
0	Accuracy	0.953271	boosted_lgbm_optimal	validation
1	Precision	0.972973	boosted_lgbm_optimal	validation
2	Recall	0.900000	boosted_lgbm_optimal	validation
3	F1	0.935065	boosted_lgbm_optimal	validation
4	AUROC	0.942537	boosted_lgbm_optimal	validation

################################## 
joblib.dump(boosted_lgbm_optimal, 
            os.path.join("..", MODELS_PATH, "boosted_model_light_gbm_optimal.pkl"))

['..\\models\\boosted_model_light_gbm_optimal.pkl']

1.7.6 CatBoost

CatBoost (Categorical Boosting) is a boosting algorithm optimized for categorical data. Unlike other gradient boosting methods that require categorical variables to be manually encoded, CatBoost handles them natively, reducing preprocessing effort and improving performance. It builds decision trees iteratively, like other boosting methods, but uses ordered boosting to prevent target leakage and enhance generalization. The main advantages of CatBoost are its ability to handle categorical data without extensive preprocessing, high accuracy with minimal tuning, and robustness against overfitting due to built-in regularization. Additionally, it is relatively fast and memory-efficient. However, CatBoost can still be slower than LightGBM on very large datasets, and while it requires less tuning, improper parameter selection can lead to suboptimal performance. Its internal mechanics, such as ordered boosting, make interpretation more complex compared to simpler models.

1. The catboost model from the catboost Python library API was implemented.
2. The model contains 4 hyperparameters for tuning:
   • learning_rate = step size at which weights are updated during training made to vary between 0.01 and 0.10
   • max_depth = maximum depth of each decision tree in the boosting process made to vary between 3 and 6
   • num_leaves = maximum tree leaves for base learners made to vary between 8 and 16
   • iterations = number of boosted trees to fit made to vary between 50 and 100
3. A special hyperparameter (scale_pos_weight = 1.7) was fixed to address the minimal 1.7:1 class imbalance observed between the B and M diagnosis categories.
4. Hyperparameter tuning was conducted using the 5-cycle 5-fold cross-validation method with optimal model performance using the F1 score determined for:
   • learning_rate = 0.1
   • min_child_samples = 6
   • num_leaves = 8
   • n_estimators = 100
5. The apparent model performance of the optimal model is summarized as follows:
   • Accuracy = 0.9968
   • Precision = 0.9916
   • Recall = 1.0000
   • F1 Score = 0.9958
   • AUROC = 0.9975
6. The independent validation model performance of the optimal model is summarized as follows:
   • Accuracy = 0.9626
   • Precision = 0.9736
   • Recall = 0.9250
   • F1 Score = 0.9487
   • AUROC = 0.9550
7. Sufficiently comparable apparent and independent validation model performance observed that might be indicative of the absence of excessive model overfitting.

##################################
# Defining the missing value imputation, scaling and PCA preprocessing parameters
##################################
scaling_pca_preprocessor = Pipeline([
    ('imputer', SimpleImputer(strategy='median')),
    ('scaler', StandardScaler()),           
    ('pca', PCA(n_components=10, random_state=987654321))  
])

##################################
# Defining the preprocessing and modeling pipeline parameters
##################################
boosted_cb_pipeline = Pipeline([
    ('scaling_pca_preprocessor', scaling_pca_preprocessor),
    ('boosted_cb_model', CatBoostClassifier(scale_pos_weight=2.0, 
                                            random_state=987654321,
                                            subsample =0.7,
                                            colsample_bylevel=0.7,
                                            grow_policy='Lossguide',
                                            verbose=0,
                                            allow_writing_files=False))
])

##################################
# Defining hyperparameter grid
##################################
boosted_cb_hyperparameter_grid = {
    'boosted_cb_model__learning_rate': [0.01, 0.10],
    'boosted_cb_model__max_depth': [3, 6], 
    'boosted_cb_model__num_leaves': [8, 16],
    'boosted_cb_model__iterations': [50, 100]
}

##################################
# Defining the cross-validation strategy (5-cycle 5-fold CV)
##################################
cv_strategy = RepeatedStratifiedKFold(n_splits=5, 
                                      n_repeats=5, 
                                      random_state=987654321)

##################################
# Performing Grid Search with cross-validation
##################################
boosted_cb_grid_search = GridSearchCV(
    estimator=boosted_cb_pipeline,
    param_grid=boosted_cb_hyperparameter_grid,
    scoring='f1',
    cv=cv_strategy,
    n_jobs=-1,
    verbose=1
)

##################################
# Encoding the response variables
# for model training and validation
##################################
y_train_encoded = y_train.map({'B': 0, 'M': 1})
y_validation_encoded = y_validation.map({'B': 0, 'M': 1})

##################################
# Fitting GridSearchCV
##################################
boosted_cb_grid_search.fit(X_train, y_train_encoded)

Fitting 25 folds for each of 16 candidates, totalling 400 fits

GridSearchCV(cv=RepeatedStratifiedKFold(n_repeats=5, n_splits=5, random_state=987654321),
             estimator=Pipeline(steps=[('scaling_pca_preprocessor',
                                        Pipeline(steps=[('imputer',
                                                         SimpleImputer(strategy='median')),
                                                        ('scaler',
                                                         StandardScaler()),
                                                        ('pca',
                                                         PCA(n_components=10,
                                                             random_state=987654321))])),
                                       ('boosted_cb_model',
                                        <catboost.core.CatBoostClassifier object at 0x00000296BF6D7800>)]),
             n_jobs=-1,
             param_grid={'boosted_cb_model__iterations': [50, 100],
                         'boosted_cb_model__learning_rate': [0.01, 0.1],
                         'boosted_cb_model__max_depth': [3, 6],
                         'boosted_cb_model__num_leaves': [8, 16]},
             scoring='f1', verbose=1)

In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook.
On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.

##################################
# Identifying the best model
##################################
boosted_cb_optimal = boosted_cb_grid_search.best_estimator_

##################################
# Evaluating the F1 scores
# on the training, cross-validation, and validation data
##################################
boosted_cb_optimal_f1_cv = boosted_cb_grid_search.best_score_
boosted_cb_optimal_f1_train = f1_score(y_train_encoded, boosted_cb_optimal.predict(X_train))
boosted_cb_optimal_f1_validation = f1_score(y_validation_encoded, boosted_cb_optimal.predict(X_validation))

##################################
# Identifying the optimal model
##################################
print('Best Boosted Model - CatBoost: ')
print(f"Best CatBoost Hyperparameters: {boosted_cb_grid_search.best_params_}")

Best Boosted Model - CatBoost: 
Best CatBoost Hyperparameters: {'boosted_cb_model__iterations': 100, 'boosted_cb_model__learning_rate': 0.1, 'boosted_cb_model__max_depth': 6, 'boosted_cb_model__num_leaves': 8}

##################################
# Summarizing the F1 score results
# and classification metrics
# on the training and cross-validated data
# to assess overfitting optimism
##################################
print(f"F1 Score on Cross-Validated Data: {boosted_cb_optimal_f1_cv:.4f}")
print(f"F1 Score on Training Data: {boosted_cb_optimal_f1_train:.4f}")
print("\nClassification Report on Train Data:\n", classification_report(y_train_encoded, boosted_cb_optimal.predict(X_train)))

F1 Score on Cross-Validated Data: 0.9295
F1 Score on Training Data: 0.9958

Classification Report on Train Data:
               precision    recall  f1-score   support

           0       1.00      0.99      1.00       200
           1       0.99      1.00      1.00       119

    accuracy                           1.00       319
   macro avg       1.00      1.00      1.00       319
weighted avg       1.00      1.00      1.00       319

##################################
# Formulating the raw and normalized
# confusion matrices
# from the train data
##################################
cm_raw = confusion_matrix(y_train_encoded, boosted_cb_optimal.predict(X_train))
cm_normalized = confusion_matrix(y_train_encoded, boosted_cb_optimal.predict(X_train), normalize='true')
fig, ax = plt.subplots(1, 2, figsize=(17, 8))
sns.heatmap(cm_raw, annot=True, fmt='d', cmap='Blues', ax=ax[0])
ax[0].set_title('Raw Confusion Matrix: Optimal CatBoost Train Performance', fontsize=11)
ax[0].set_xlabel('Predicted')
ax[0].set_ylabel('Actual')
sns.heatmap(cm_normalized, annot=True, fmt='.2f', cmap='Blues', ax=ax[1])
ax[1].set_title('Normalized Confusion Matrix: Optimal CatBoost Train Performance', fontsize=11)
ax[1].set_xlabel('Predicted')
ax[1].set_ylabel('Actual')
plt.tight_layout()
plt.show()

##################################
# Summarizing the F1 score results
# and classification metrics
# on the validation data
# to assess overfitting optimism
##################################
print(f"F1 Score on Validation Data: {boosted_cb_optimal_f1_validation:.4f}")
print("\nClassification Report on Validation Data:\n", classification_report(y_validation_encoded, boosted_cb_optimal.predict(X_validation)))

F1 Score on Validation Data: 0.9487

Classification Report on Validation Data:
               precision    recall  f1-score   support

           0       0.96      0.99      0.97        67
           1       0.97      0.93      0.95        40

    accuracy                           0.96       107
   macro avg       0.97      0.96      0.96       107
weighted avg       0.96      0.96      0.96       107

##################################
# Formulating the raw and normalized
# confusion matrices
# from the validation data
##################################
cm_raw = confusion_matrix(y_validation_encoded, boosted_cb_optimal.predict(X_validation))
cm_normalized = confusion_matrix(y_validation_encoded, boosted_cb_optimal.predict(X_validation), normalize='true')
fig, ax = plt.subplots(1, 2, figsize=(17, 8))
sns.heatmap(cm_raw, annot=True, fmt='d', cmap='Blues', ax=ax[0])
ax[0].set_title('Raw Confusion Matrix: Optimal CatBoost Validation Performance', fontsize=11)
ax[0].set_xlabel('Predicted')
ax[0].set_ylabel('Actual')
sns.heatmap(cm_normalized, annot=True, fmt='.2f', cmap='Blues', ax=ax[1])
ax[1].set_title('Normalized Confusion Matrix: Optimal CatBoost Validation Performance', fontsize=11)
ax[1].set_xlabel('Predicted')
ax[1].set_ylabel('Actual')
plt.tight_layout()
plt.show()

##################################
# Gathering the model evaluation metrics
# for the train data
##################################
boosted_cb_optimal_train = model_performance_evaluation(y_train_encoded, boosted_cb_optimal.predict(X_train))
boosted_cb_optimal_train['model'] = ['boosted_cb_optimal'] * 5
boosted_cb_optimal_train['set'] = ['train'] * 5
print('Optimal CatBoost Train Performance Metrics: ')
display(boosted_cb_optimal_train)

Optimal CatBoost Train Performance Metrics: 

	metric_name	metric_value	model	set
0	Accuracy	0.996865	boosted_cb_optimal	train
1	Precision	0.991667	boosted_cb_optimal	train
2	Recall	1.000000	boosted_cb_optimal	train
3	F1	0.995816	boosted_cb_optimal	train
4	AUROC	0.997500	boosted_cb_optimal	train

##################################
# Gathering the model evaluation metrics
# for the validation data
##################################
boosted_cb_optimal_validation = model_performance_evaluation(y_validation_encoded, boosted_cb_optimal.predict(X_validation))
boosted_cb_optimal_validation['model'] = ['boosted_cb_optimal'] * 5
boosted_cb_optimal_validation['set'] = ['validation'] * 5
print('Optimal CatBoost Validation Performance Metrics: ')
display(boosted_cb_optimal_validation)

Optimal CatBoost Validation Performance Metrics: 

	metric_name	metric_value	model	set
0	Accuracy	0.962617	boosted_cb_optimal	validation
1	Precision	0.973684	boosted_cb_optimal	validation
2	Recall	0.925000	boosted_cb_optimal	validation
3	F1	0.948718	boosted_cb_optimal	validation
4	AUROC	0.955037	boosted_cb_optimal	validation

##################################
# Saving the best individual model
# developed from the train data
################################## 
joblib.dump(boosted_cb_optimal, 
            os.path.join("..", MODELS_PATH, "boosted_model_catboost_optimal.pkl"))

['..\\models\\boosted_model_catboost_optimal.pkl']

1.8. Model Selection

1. Among 6 candidate models, the Categorical Boosting Model was selected as the final model by demonstrating the best F1 Score for the independent validation data with minimal overfitting :
   • Apparent F1 Score Performance = 0.9958
   • Independent Validation F1 Score Performance = 0.9487
2. The final model similarly demonstrated consistently high F1 Score for the test data :
   • Independent Test F1 Score Performance = 0.9549
3. The final model configuration is described as follows:
   • catboost with optimal hyperparameters:
     • learning_rate = 0.1
     • min_child_samples = 6
     • num_leaves = 8
     • n_estimators = 100

##################################
# Consolidating all the
# bagged, boosted, stacked and blended
# model performance measures
# for the train and validation data
##################################
ensemble_train_validation_all_performance = pd.concat([bagged_rf_optimal_train,
                                             bagged_rf_optimal_validation,                                            
                                             boosted_ab_optimal_train,
                                             boosted_ab_optimal_validation,
                                             boosted_gb_optimal_train,
                                             boosted_gb_optimal_validation,
                                             boosted_xgb_optimal_train,
                                             boosted_xgb_optimal_validation,
                                             boosted_lgbm_optimal_train,
                                             boosted_lgbm_optimal_validation,
                                             boosted_cb_optimal_train,
                                             boosted_cb_optimal_validation], 
                                            ignore_index=True)
print('Consolidated Ensemble Model Performance on Train and Validation Data: ')
display(ensemble_train_validation_all_performance)

Consolidated Ensemble Model Performance on Train and Validation Data: 

	metric_name	metric_value	model	set
0	Accuracy	0.974922	bagged_rf_optimal	train
1	Precision	0.974359	bagged_rf_optimal	train
2	Recall	0.957983	bagged_rf_optimal	train
3	F1	0.966102	bagged_rf_optimal	train
4	AUROC	0.971492	bagged_rf_optimal	train
5	Accuracy	0.934579	bagged_rf_optimal	validation
6	Precision	0.971429	bagged_rf_optimal	validation
7	Recall	0.850000	bagged_rf_optimal	validation
8	F1	0.906667	bagged_rf_optimal	validation
9	AUROC	0.917537	bagged_rf_optimal	validation
10	Accuracy	0.993730	boosted_ab_optimal	train
11	Precision	1.000000	boosted_ab_optimal	train
12	Recall	0.983193	boosted_ab_optimal	train
13	F1	0.991525	boosted_ab_optimal	train
14	AUROC	0.991597	boosted_ab_optimal	train
15	Accuracy	0.943925	boosted_ab_optimal	validation
16	Precision	0.972222	boosted_ab_optimal	validation
17	Recall	0.875000	boosted_ab_optimal	validation
18	F1	0.921053	boosted_ab_optimal	validation
19	AUROC	0.930037	boosted_ab_optimal	validation
20	Accuracy	1.000000	boosted_gb_optimal	train
21	Precision	1.000000	boosted_gb_optimal	train
22	Recall	1.000000	boosted_gb_optimal	train
23	F1	1.000000	boosted_gb_optimal	train
24	AUROC	1.000000	boosted_gb_optimal	train
25	Accuracy	0.934579	boosted_gb_optimal	validation
26	Precision	0.971429	boosted_gb_optimal	validation
27	Recall	0.850000	boosted_gb_optimal	validation
28	F1	0.906667	boosted_gb_optimal	validation
29	AUROC	0.917537	boosted_gb_optimal	validation
30	Accuracy	1.000000	boosted_xgb_optimal	train
31	Precision	1.000000	boosted_xgb_optimal	train
32	Recall	1.000000	boosted_xgb_optimal	train
33	F1	1.000000	boosted_xgb_optimal	train
34	AUROC	1.000000	boosted_xgb_optimal	train
35	Accuracy	0.943925	boosted_xgb_optimal	validation
36	Precision	0.972222	boosted_xgb_optimal	validation
37	Recall	0.875000	boosted_xgb_optimal	validation
38	F1	0.921053	boosted_xgb_optimal	validation
39	AUROC	0.930037	boosted_xgb_optimal	validation
40	Accuracy	1.000000	boosted_lgbm_optimal	train
41	Precision	1.000000	boosted_lgbm_optimal	train
42	Recall	1.000000	boosted_lgbm_optimal	train
43	F1	1.000000	boosted_lgbm_optimal	train
44	AUROC	1.000000	boosted_lgbm_optimal	train
45	Accuracy	0.953271	boosted_lgbm_optimal	validation
46	Precision	0.972973	boosted_lgbm_optimal	validation
47	Recall	0.900000	boosted_lgbm_optimal	validation
48	F1	0.935065	boosted_lgbm_optimal	validation
49	AUROC	0.942537	boosted_lgbm_optimal	validation
50	Accuracy	0.996865	boosted_cb_optimal	train
51	Precision	0.991667	boosted_cb_optimal	train
52	Recall	1.000000	boosted_cb_optimal	train
53	F1	0.995816	boosted_cb_optimal	train
54	AUROC	0.997500	boosted_cb_optimal	train
55	Accuracy	0.962617	boosted_cb_optimal	validation
56	Precision	0.973684	boosted_cb_optimal	validation
57	Recall	0.925000	boosted_cb_optimal	validation
58	F1	0.948718	boosted_cb_optimal	validation
59	AUROC	0.955037	boosted_cb_optimal	validation

##################################
# Consolidating all the F1 score
# model performance measures
# between the train and validation data
##################################
ensemble_train_validation_all_performance_F1 = ensemble_train_validation_all_performance[ensemble_train_validation_all_performance['metric_name']=='F1']
ensemble_train_validation_all_performance_F1_train = ensemble_train_validation_all_performance_F1[ensemble_train_validation_all_performance_F1['set']=='train'].loc[:,"metric_value"]
ensemble_train_validation_all_performance_F1_validation = ensemble_train_validation_all_performance_F1[ensemble_train_validation_all_performance_F1['set']=='validation'].loc[:,"metric_value"]

##################################
# Combining all the F1 score
# model performance measures
# between the train and validation data
##################################
ensemble_train_validation_all_performance_F1_plot = pd.DataFrame({'train': ensemble_train_validation_all_performance_F1_train.values,
                                                              'validation': ensemble_train_validation_all_performance_F1_validation.values},
                                                             index=ensemble_train_validation_all_performance_F1['model'].unique())
ensemble_train_validation_all_performance_F1_plot

	train	validation
bagged_rf_optimal	0.966102	0.906667
boosted_ab_optimal	0.991525	0.921053
boosted_gb_optimal	1.000000	0.906667
boosted_xgb_optimal	1.000000	0.921053
boosted_lgbm_optimal	1.000000	0.935065
boosted_cb_optimal	0.995816	0.948718

##################################
# Plotting all the F1 score
# model performance measures
# between the train and validation sets
##################################
ensemble_train_validation_all_performance_F1_plot = ensemble_train_validation_all_performance_F1_plot.plot.barh(figsize=(10, 7), width=0.9)
ensemble_train_validation_all_performance_F1_plot.set_xlim(0.00,1.00)
ensemble_train_validation_all_performance_F1_plot.set_title("Model Comparison by F1 Score Performance on Train and Validation Data")
ensemble_train_validation_all_performance_F1_plot.set_xlabel("F1 Score Performance")
ensemble_train_validation_all_performance_F1_plot.set_ylabel("Ensemble Model")
ensemble_train_validation_all_performance_F1_plot.grid(False)
ensemble_train_validation_all_performance_F1_plot.legend(loc='center left', bbox_to_anchor=(1.0, 0.5))
for container in ensemble_train_validation_all_performance_F1_plot.containers:
    ensemble_train_validation_all_performance_F1_plot.bar_label(container, fmt='%.5f', padding=-50, color='white', fontweight='bold')

##################################
# Gathering all model performance measures
# for the validation data
##################################
ensemble_train_validation_all_performance_Accuracy_validation = ensemble_train_validation_all_performance[(ensemble_train_validation_all_performance['set']=='validation') & (ensemble_train_validation_all_performance['metric_name']=='Accuracy')].loc[:,"metric_value"]
ensemble_train_validation_all_performance_Precision_validation = ensemble_train_validation_all_performance[(ensemble_train_validation_all_performance['set']=='validation') & (ensemble_train_validation_all_performance['metric_name']=='Precision')].loc[:,"metric_value"]
ensemble_train_validation_all_performance_Recall_validation = ensemble_train_validation_all_performance[(ensemble_train_validation_all_performance['set']=='validation') & (ensemble_train_validation_all_performance['metric_name']=='Recall')].loc[:,"metric_value"]
ensemble_train_validation_all_performance_F1_validation = ensemble_train_validation_all_performance[(ensemble_train_validation_all_performance['set']=='validation') & (ensemble_train_validation_all_performance['metric_name']=='F1')].loc[:,"metric_value"]
ensemble_train_validation_all_performance_AUROC_validation = ensemble_train_validation_all_performance[(ensemble_train_validation_all_performance['set']=='validation') & (ensemble_train_validation_all_performance['metric_name']=='AUROC')].loc[:,"metric_value"]

##################################
# Combining all the model performance measures
# for the validation data
##################################
ensemble_train_validation_all_performance_all_plot_validation = pd.DataFrame({'accuracy': ensemble_train_validation_all_performance_Accuracy_validation.values,
                                                                    'precision': ensemble_train_validation_all_performance_Precision_validation.values,
                                                                    'recall': ensemble_train_validation_all_performance_Recall_validation.values,
                                                                    'f1': ensemble_train_validation_all_performance_F1_validation.values,
                                                                    'auroc': ensemble_train_validation_all_performance_AUROC_validation.values},
                                                                   index=ensemble_train_validation_all_performance['model'].unique())
ensemble_train_validation_all_performance_all_plot_validation

	accuracy	precision	recall	f1	auroc
bagged_rf_optimal	0.934579	0.971429	0.850	0.906667	0.917537
boosted_ab_optimal	0.943925	0.972222	0.875	0.921053	0.930037
boosted_gb_optimal	0.934579	0.971429	0.850	0.906667	0.917537
boosted_xgb_optimal	0.943925	0.972222	0.875	0.921053	0.930037
boosted_lgbm_optimal	0.953271	0.972973	0.900	0.935065	0.942537
boosted_cb_optimal	0.962617	0.973684	0.925	0.948718	0.955037

##################################
# Gathering the model evaluation metrics
# for the test data
##################################
##################################
# Defining a dictionary of models and 
# their corresponding optimal model functions
##################################
models = {
    'bagged_rf_optimal': bagged_rf_optimal,
    'boosted_ab_optimal': boosted_ab_optimal,
    'boosted_gb_optimal': boosted_gb_optimal,
    'boosted_xgb_optimal': boosted_xgb_optimal,
    'boosted_lgbm_optimal': boosted_lgbm_optimal,
    'boosted_cb_optimal': boosted_cb_optimal
}

##################################
# Encoding the response variables
# for model testing
##################################
y_test_encoded = y_test.map({'B': 0, 'M': 1})

##################################
# Storing the model evaluation metrics
# for the test data
##################################
ensemble_test_all_performance = []

##################################
# Looping through each model 
# and evaluate performance on test data
##################################
for model_name, model in models.items():
   
    # Evaluating performance
    ensemble_test_all_performance_results = model_performance_evaluation(y_test_encoded, model.predict(X_test))
    
    # Adding metadata columns
    ensemble_test_all_performance_results['model'] = model_name
    ensemble_test_all_performance_results['set'] = 'test'
    
    # Storing result
    ensemble_test_all_performance.append(ensemble_test_all_performance_results)
    

##################################
# Consolidating all model performance measures
# for the test data
##################################
ensemble_test_all_performance = pd.concat(ensemble_test_all_performance, ignore_index=True)
print('Consolidated Ensemble Model Performance on Test Data: ')
display(ensemble_test_all_performance)

Consolidated Ensemble Model Performance on Test Data: 

	metric_name	metric_value	model	set
0	Accuracy	0.944056	bagged_rf_optimal	test
1	Precision	0.941176	bagged_rf_optimal	test
2	Recall	0.905660	bagged_rf_optimal	test
3	F1	0.923077	bagged_rf_optimal	test
4	AUROC	0.936164	bagged_rf_optimal	test
5	Accuracy	0.979021	boosted_ab_optimal	test
6	Precision	0.980769	boosted_ab_optimal	test
7	Recall	0.962264	boosted_ab_optimal	test
8	F1	0.971429	boosted_ab_optimal	test
9	AUROC	0.975577	boosted_ab_optimal	test
10	Accuracy	0.965035	boosted_gb_optimal	test
11	Precision	0.944444	boosted_gb_optimal	test
12	Recall	0.962264	boosted_gb_optimal	test
13	F1	0.953271	boosted_gb_optimal	test
14	AUROC	0.964465	boosted_gb_optimal	test
15	Accuracy	0.965035	boosted_xgb_optimal	test
16	Precision	0.944444	boosted_xgb_optimal	test
17	Recall	0.962264	boosted_xgb_optimal	test
18	F1	0.953271	boosted_xgb_optimal	test
19	AUROC	0.964465	boosted_xgb_optimal	test
20	Accuracy	0.979021	boosted_lgbm_optimal	test
21	Precision	0.962963	boosted_lgbm_optimal	test
22	Recall	0.981132	boosted_lgbm_optimal	test
23	F1	0.971963	boosted_lgbm_optimal	test
24	AUROC	0.979455	boosted_lgbm_optimal	test
25	Accuracy	0.965035	boosted_cb_optimal	test
26	Precision	0.913793	boosted_cb_optimal	test
27	Recall	1.000000	boosted_cb_optimal	test
28	F1	0.954955	boosted_cb_optimal	test
29	AUROC	0.972222	boosted_cb_optimal	test

##################################
# Gathering all model performance measures
# for the test data
##################################
ensemble_test_all_performance_Accuracy_test = ensemble_test_all_performance[(ensemble_test_all_performance['set']=='test') & (ensemble_test_all_performance['metric_name']=='Accuracy')].loc[:,"metric_value"]
ensemble_test_all_performance_Precision_test = ensemble_test_all_performance[(ensemble_test_all_performance['set']=='test') & (ensemble_test_all_performance['metric_name']=='Precision')].loc[:,"metric_value"]
ensemble_test_all_performance_Recall_test = ensemble_test_all_performance[(ensemble_test_all_performance['set']=='test') & (ensemble_test_all_performance['metric_name']=='Recall')].loc[:,"metric_value"]
ensemble_test_all_performance_F1_test = ensemble_test_all_performance[(ensemble_test_all_performance['set']=='test') & (ensemble_test_all_performance['metric_name']=='F1')].loc[:,"metric_value"]
ensemble_test_all_performance_AUROC_test = ensemble_test_all_performance[(ensemble_test_all_performance['set']=='test') & (ensemble_test_all_performance['metric_name']=='AUROC')].loc[:,"metric_value"]

##################################
# Combining all the model performance measures
# for the test data
##################################
ensemble_test_all_performance_all_plot_test = pd.DataFrame({'accuracy': ensemble_test_all_performance_Accuracy_test.values,
                                                            'precision': ensemble_test_all_performance_Precision_test.values,
                                                            'recall': ensemble_test_all_performance_Recall_test.values,
                                                            'f1': ensemble_test_all_performance_F1_test.values,
                                                            'auroc': ensemble_test_all_performance_AUROC_test.values},
                                                           index=ensemble_test_all_performance['model'].unique())
ensemble_test_all_performance_all_plot_test

	accuracy	precision	recall	f1	auroc
bagged_rf_optimal	0.944056	0.941176	0.905660	0.923077	0.936164
boosted_ab_optimal	0.979021	0.980769	0.962264	0.971429	0.975577
boosted_gb_optimal	0.965035	0.944444	0.962264	0.953271	0.964465
boosted_xgb_optimal	0.965035	0.944444	0.962264	0.953271	0.964465
boosted_lgbm_optimal	0.979021	0.962963	0.981132	0.971963	0.979455
boosted_cb_optimal	0.965035	0.913793	1.000000	0.954955	0.972222

##################################
# Consolidating all the final
# bagged, boosted, stacked and blended
# model performance measures
# for the train, validation and test data
##################################
ensemble_overall_performance = pd.concat([ensemble_train_validation_all_performance, ensemble_test_all_performance], axis=0)

##################################
# Consolidating all the F1 score
# model performance measures
# between the train, validation and test data
##################################
ensemble_overall_performance_F1 = ensemble_overall_performance[ensemble_overall_performance['metric_name']=='F1']
ensemble_overall_performance_F1_train = ensemble_overall_performance_F1[ensemble_overall_performance_F1['set']=='train'].loc[:,"metric_value"]
ensemble_overall_performance_F1_validation = ensemble_overall_performance_F1[ensemble_overall_performance_F1['set']=='validation'].loc[:,"metric_value"]
ensemble_overall_performance_F1_test = ensemble_overall_performance_F1[ensemble_overall_performance_F1['set']=='test'].loc[:,"metric_value"]

##################################
# Combining all the F1 score
# model performance measures
# between the train and validation data
##################################
ensemble_overall_performance_F1_plot = pd.DataFrame({'train': ensemble_overall_performance_F1_train.values,
                                                     'validation': ensemble_overall_performance_F1_validation.values,
                                                     'test': ensemble_overall_performance_F1_test.values},
                                                    index=ensemble_overall_performance_F1['model'].unique())
ensemble_overall_performance_F1_plot

	train	validation	test
bagged_rf_optimal	0.966102	0.906667	0.923077
boosted_ab_optimal	0.991525	0.921053	0.971429
boosted_gb_optimal	1.000000	0.906667	0.953271
boosted_xgb_optimal	1.000000	0.921053	0.953271
boosted_lgbm_optimal	1.000000	0.935065	0.971963
boosted_cb_optimal	0.995816	0.948718	0.954955

##################################
# Plotting all the F1 score
# model performance measures
# between train, validation and test sets
##################################
ensemble_overall_performance_F1_plot = ensemble_overall_performance_F1_plot.plot.barh(figsize=(10, 8), width=0.9)
ensemble_overall_performance_F1_plot.set_xlim(0.00,1.00)
ensemble_overall_performance_F1_plot.set_title("Model Comparison by F1 Score Performance on Train, Validation and Test Data")
ensemble_overall_performance_F1_plot.set_xlabel("F1 Score Performance")
ensemble_overall_performance_F1_plot.set_ylabel("Ensemble Model")
ensemble_overall_performance_F1_plot.grid(False)
ensemble_overall_performance_F1_plot.legend(loc='center left', bbox_to_anchor=(1.0, 0.5))
for container in ensemble_overall_performance_F1_plot.containers:
    ensemble_overall_performance_F1_plot.bar_label(container, fmt='%.5f', padding=-50, color='white', fontweight='bold')

1.9. Model Monitoring using the NannyML Framework

1.9.1 Simulated Baseline Control

##################################
# Defining the global parameters
# for the post-model deployment scenario simulation
##################################
N_CHUNKS = 10
CHUNK_SIZE = 100
RANDOM_STATE = 987654321
TARGET_COL = 'diagnosis'
LABEL_MAP = {'B': 0, 'M': 1}
FEATURE_COLUMNS = [
'radius_mean','texture_mean','perimeter_mean','area_mean','smoothness_mean',
'compactness_mean','concavity_mean','concave points_mean','symmetry_mean','fractal_dimension_mean',
'radius_se','texture_se','perimeter_se','area_se','smoothness_se',
'compactness_se','concavity_se','concave points_se','symmetry_se','fractal_dimension_se',
'radius_worst','texture_worst','perimeter_worst','area_worst','smoothness_worst',
'compactness_worst','concavity_worst','concave points_worst','symmetry_worst','fractal_dimension_worst'
]

##################################
# Creating the monitoring baseline control
# by combining both validation and test data together
##################################
breast_cancer_monitoring_baseline = pd.concat(
    [breast_cancer_validation, breast_cancer_test], 
    axis=0,            
    ignore_index=True
)

##################################
# Defining a function for generating
# a post-model data stream simulation
##################################
def make_stream_from_dataframe(df, n_chunks=N_CHUNKS, chunk_size=CHUNK_SIZE, random_state=RANDOM_STATE):
    """Creates a synthetic ordered stream (chunks) including at least one instance of both 'M' and 'B' classes."""
    # Initialiing a random number generator for reproducibility
    rng = np.random.RandomState(random_state)
    # Initializing an empty list to store each generated chunk
    rows = []

    # Splitting the dataframe into the two classes
    df_M = df[df[TARGET_COL] == "M"]
    df_B = df[df[TARGET_COL] == "B"]

    # Determining roughly balanced counts per chunk
    half_size = chunk_size // 2
    
    # Iterating through the desired number of chunks (simulated time intervals)
    for chunk_idx in range(n_chunks):
        # Sampling half of the chunk from each class (with replacement)
        sample_M = df_M.sample(
            n=half_size, replace=True, random_state=rng.randint(0, 2**31 - 1)
        )
        sample_B = df_B.sample(
            n=chunk_size - half_size, replace=True, random_state=rng.randint(0, 2**31 - 1)
        )

        # Combining, shuffling, and labeling with chunk/time index
        chunk = pd.concat([sample_M, sample_B], ignore_index=True).sample(
            frac=1, random_state=rng.randint(0, 2**31 - 1)
        )
        chunk["__chunk"] = chunk_idx
        chunk["__timestamp"] = chunk_idx

        rows.append(chunk)
    # Combining all chunks into a single DataFrame that represents a continuous data stream
    return pd.concat(rows, ignore_index=True)

##################################
# Defining a function for 
# computing model predictions and probabilities
# using the final selected model - categorical boosting model
##################################
def compute_preds_and_proba(pipeline, X):
    """Returns predicted labels and class 1 probabilities"""
    # Generating predicted class labels (0 or 1) using the trained model pipeline
    y_pred = pipeline.predict(X)
    try:
        # Obtaining the probability of the positive class (class 1)
        y_proba = pipeline.predict_proba(X)[:, 1]
    except Exception:
        # Computing the probability approximation if predict_proba is unavailable
        y_proba = 1 / (1 + np.exp(-pipeline.decision_function(X)))
    # Returning both predicted labels and corresponding class-1 probabilities
    return y_pred, y_proba

##################################
# Defining a function for 
# simulating the baseline control
##################################
def simulate_P1_baseline(df):
    # Creating a time-ordered synthetic stream of data chunks
    return make_stream_from_dataframe(df)
    

##################################
# Defining a function for 
# plotting chunk-based boxplots for selected features
# for baseline control
##################################
sns.set(style="whitegrid", context="notebook")

def plot_baseline_feature_boxplot(df_base, features, scenario_name="Baseline"):
    """Chunk-based boxplots for selected features in baseline."""
    n_features = len(features)
    fig, axes = plt.subplots(n_features, 1, figsize=(12, 3 * n_features), sharex=True)
    if n_features == 1:
        axes = [axes]
    for ax, f in zip(axes, features):
        sns.boxplot(
            data=df_base,
            x="__chunk", y=f, ax=ax, showfliers=False, color="#4C72B0"
        )
        ax.set_title(f"Chunk-wise {f}: {scenario_name}")
        ax.set_xlabel("Chunk Index (Simulated Time)")
        ax.set_ylabel(f)
        ax.set_xticks(range(10))
    plt.tight_layout()
    plt.show()

##################################
# Defining a function for 
# plotting feature mean per chunk
# for baseline control
##################################
def plot_baseline_feature_mean_line(df_base, features, scenario_name="Baseline"):
    """Plots per-feature mean values over chunks (one chart per feature)."""
    mean_values = df_base.groupby('__chunk')[features].mean()
    
    n_features = len(features)
    fig, axes = plt.subplots(n_features, 1, figsize=(12, 3 * n_features), sharex=True)
    if n_features == 1:
        axes = [axes]

    for ax, f in zip(axes, features):
        sns.lineplot(x=mean_values.index, y=mean_values[f], color="#4C72B0", ax=ax)
        ax.set_title(f"Chunk-wise Mean of {f} ({scenario_name})", fontsize=11)
        ax.set_xlabel("Chunk Index")
        ax.set_ylabel("Mean Value")
        ax.grid(True, alpha=0.3)
        ax.set_xticks(range(10))
    
    plt.tight_layout()
    plt.show()

##################################
# Defining a function for 
# plotting class proportion ('M' vs 'B') across chunks
# for baseline control
##################################
def plot_baseline_class_proportion(df_base, scenario_name="Baseline"):
    """Class proportion ('M' vs 'B') across chunks for baseline."""
    prop = df_base.groupby('__chunk')['diagnosis'].value_counts(normalize=True).unstack().fillna(0)
    fig, ax = plt.subplots(figsize=(14, 3))
    sns.lineplot(data=prop['M'], label="Proportion of 'M'", color="#4C72B0", ax=ax)
    ax.set_title(f"Class Proportion per Chunk: {scenario_name}")
    ax.set_xlabel("Chunk Index")
    ax.set_ylabel("Proportion of 'M'")
    ax.set_ylim(-0.1, 1)
    ax.set_xticks(range(10))
    plt.show()

##################################
# Defining a function for 
# plotting missing fraction per chunk
# for baseline control
##################################
def plot_baseline_missingness(df_base, features, scenario_name="Baseline"):
    """Missing fraction per chunk for selected features, one plot per feature."""
    miss = df_base.groupby('__chunk')[features].apply(lambda x: x.isna().mean())
    
    n_features = len(features)
    fig, axes = plt.subplots(n_features, 1, figsize=(12, 3 * n_features), sharex=True)
    if n_features == 1:
        axes = [axes]

    for ax, f in zip(axes, features):
        sns.lineplot(x=miss.index, y=miss[f], color="#4C72B0", ax=ax)
        ax.set_title(f"Missingness over Time: {f} ({scenario_name})", fontsize=11)
        ax.set_xlabel("Chunk Index")
        ax.set_ylabel("Missing Fraction")
        ax.set_ylim(-0.1, 1)
        ax.set_xticks(range(10))
        ax.grid(True, alpha=0.3)
    
    plt.tight_layout()
    plt.show()

    

##################################
# Simulating post-deployment data drift scenario 1 = baseline control
##################################
p1 = simulate_P1_baseline(breast_cancer_monitoring_baseline)

##################################
# Exploring the simulated baseline control
##################################
display(p1)

	diagnosis	radius_mean	texture_mean	perimeter_mean	area_mean	smoothness_mean	compactness_mean	concavity_mean	concave points_mean	symmetry_mean	...	perimeter_worst	area_worst	smoothness_worst	compactness_worst	concavity_worst	concave points_worst	symmetry_worst	fractal_dimension_worst	__chunk	__timestamp
0	M	17.420	25.56	114.50	948.0	0.10060	0.11460	0.168200	0.065970	0.1308	...	120.40	1021.0	0.1243	0.17930	0.280300	0.10990	0.1603	0.06818	0	0
1	M	22.270	19.67	152.80	1509.0	0.13260	0.27680	0.426400	0.182300	0.2556	...	206.80	2360.0	0.1701	0.69970	0.960800	0.29100	0.4055	0.09789	0	0
2	B	11.250	14.78	71.38	390.0	0.08306	0.04458	0.000974	0.002941	0.1773	...	82.08	492.7	0.1166	0.09794	0.005518	0.01667	0.2815	0.07418	0	0
3	B	12.250	22.44	78.18	466.5	0.08192	0.05200	0.017140	0.012610	0.1544	...	92.74	622.9	0.1256	0.18040	0.123000	0.06335	0.3100	0.08203	0	0
4	B	10.480	19.86	66.72	337.7	0.10700	0.05971	0.048310	0.030700	0.1737	...	73.68	402.8	0.1515	0.10260	0.118100	0.06736	0.2883	0.07748	0	0
...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...
995	B	14.030	21.25	89.79	603.4	0.09070	0.06945	0.014620	0.018960	0.1517	...	98.27	715.5	0.1287	0.15130	0.062310	0.07963	0.2226	0.07617	9	9
996	B	13.710	18.68	88.73	571.0	0.09916	0.10700	0.053850	0.037830	0.1714	...	99.43	701.9	0.1425	0.25660	0.193500	0.12840	0.2849	0.09031	9	9
997	B	13.080	15.71	85.63	520.0	0.10750	0.12700	0.045680	0.031100	0.1967	...	96.09	630.5	0.1312	0.27760	0.189000	0.07283	0.3184	0.08183	9	9
998	B	8.597	18.60	54.09	221.2	0.10740	0.05847	0.000000	0.000000	0.2163	...	56.65	240.1	0.1347	0.07767	0.000000	0.00000	0.3142	0.08116	9	9
999	M	19.790	25.12	130.40	1192.0	0.10150	0.15890	0.254500	0.114900	0.2202	...	148.70	1589.0	0.1275	0.38610	0.567300	0.17320	0.3305	0.08465	9	9

1000 rows × 33 columns

##################################
# Visualizing feature variability
# for baseline control
##################################
plot_baseline_feature_boxplot(p1, FEATURE_COLUMNS)

##################################
# Visualizing feature variability
# for baseline control
##################################
plot_baseline_feature_mean_line(p1, FEATURE_COLUMNS)

##################################
# Inspecting baseline class balance stability
# for baseline control
##################################
plot_baseline_class_proportion(p1)

##################################
# Evaluating baseline missingness
# for baseline control
##################################
plot_baseline_missingness(p1, FEATURE_COLUMNS)

##################################
# Fitting a drift calculator
# Using the simulated baseline control as the reference dataset
##################################
p1_univariate_drift_df = p1.copy()

##################################
# Defining a function for fitting
# a drift calculator using the simulated baseline control and
# detecting univariate drift for a given scenario
##################################
def detect_univariate_drift(baseline_df, scenario_df, feature_columns, scenario_name="Scenario"):
    """
    Fits a UnivariateDriftCalculator on baseline data and detects drift on scenario data.
    """

    # Initializing the univariate drift calculator
    univariate_drift_calculator = nml.drift.UnivariateDriftCalculator(
        column_names=feature_columns,
        treat_as_categorical=None,
        continuous_methods=["kolmogorov_smirnov"]
    )

    # Fitting the univariate drift calculator on the baseline control
    univariate_drift_calculator.fit(baseline_df)

    # Detecting univaraite drift on the scenario dataset
    results = univariate_drift_calculator.calculate(
        data=scenario_df
    )

    # Summarizing the drift detection results
    summary = results.filter(period="analysis").to_df()
    print(f"Univariate drift visualization generated for {scenario_name}")
    print(summary.head(10))

    return results
    

##################################
# Defining a function for visualizing
# univariate drift for a given scenario
##################################
def plot_univariate_drift_summary(drift_results, feature_columns, scenario_name="Scenario"):
    """
    Visualize KS statistics vs threshold per feature and summarize drift counts.
    """
    # Converting results to a DataFrame
    df = drift_results.to_df().copy()

    # Handling MultiIndex columns
    if isinstance(df.columns, pd.MultiIndex):
        df.columns = ['__'.join(col).strip() if isinstance(col, tuple) else col for col in df.columns]

    # Extracting chunk_index
    chunk_col_candidates = ["chunk__chunk__chunk_index", "chunk_index"]
    for col in chunk_col_candidates:
        if col in df.columns:
            df["chunk_index"] = df[col]
            break
    else:
        if "chunk_index" in df.index.names:
            df = df.reset_index()
        if "chunk_index" not in df.columns:
            raise KeyError("Cannot find 'chunk_index' in drift_results output.")

    # Identifying the KS value, threshold, and alert columns
    value_col = [c for c in df.columns if c.endswith("__kolmogorov_smirnov__value")]
    upper_threshold_col = [c for c in df.columns if c.endswith("__kolmogorov_smirnov__upper_threshold")]
    alert_col = [c for c in df.columns if c.endswith("__kolmogorov_smirnov__alert")]

    if not value_col or not upper_threshold_col:
        raise KeyError("Cannot find KS statistic or threshold columns in drift_results output.")

    value_col = value_col[0]
    thresh_col = upper_threshold_col[0]

    # Plotting all features row-wise
    n_features = len(feature_columns)
    fig, axes = plt.subplots(n_features, 1, figsize=(12, 3 * n_features), sharex=True)
    if n_features == 1:
        axes = [axes]

    sns.set_style("whitegrid")

    for ax, feature in zip(axes, feature_columns):
        # Finding the corresponding KS column in the dataframe
        ks_col_name = f"{feature}__kolmogorov_smirnov__value"
        thresh_col_name = f"{feature}__kolmogorov_smirnov__upper_threshold"
        if ks_col_name not in df.columns or thresh_col_name not in df.columns:
            print(f"Warning: {feature} not found in drift results. Skipping.")
            continue

        subdf = df[["chunk_index", ks_col_name, thresh_col_name]].copy()
        subdf.columns = ["chunk_index", "statistic", "threshold"]

        sns.lineplot(
            data=subdf,
            x="chunk_index",
            y="statistic",
            color="blue",
            ax=ax,
            label="KS Statistic"
        )
        ax.axhline(
            y=subdf["threshold"].iloc[0],
            color="red",
            linestyle="--",
            label="Threshold"
        )
        ax.set_title(f"{feature} ({scenario_name})", fontsize=10)
        ax.set_ylabel("KS Statistic")
        ax.set_xlabel("Chunk Index")
        ax.legend(loc="upper right", fontsize=8)
        ax.set_xticks(range(10))
        ax.grid(True, alpha=0.3)
        ax.set_ylim(-0.05, 1.05)

    plt.tight_layout()
    plt.show()

    # Formulating the summary table indicating the number of chunks exceeding threshold per feature
    univariate_drift_summary_list = []
    for feature in feature_columns:
        ks_col_name = f"{feature}__kolmogorov_smirnov__value"
        thresh_col_name = f"{feature}__kolmogorov_smirnov__upper_threshold"
        if ks_col_name not in df.columns or thresh_col_name not in df.columns:
            drift_count = 0
        else:
            drift_count = (df[ks_col_name] > df[thresh_col_name]).sum()
        univariate_drift_summary_list.append({"feature": feature, "chunk_drift_count": drift_count})

    univariate_drift_summary = pd.DataFrame(univariate_drift_summary_list)

    print("Univariate Drift Summary Table:")
    display(univariate_drift_summary)

    return univariate_drift_summary
    

##################################
# Detecting univariate drift for baseline control
##################################
univariate_drift_analysis_p1 = detect_univariate_drift(p1, p1, FEATURE_COLUMNS, "Baseline Control")

Univariate drift visualization generated for Baseline Control
       chunk                                                                  \
       chunk                                                                   
         key chunk_index start_index end_index start_date end_date    period   
0     [0:99]           0           0        99       None     None  analysis   
1  [100:199]           1         100       199       None     None  analysis   
2  [200:299]           2         200       299       None     None  analysis   
3  [300:399]           3         300       399       None     None  analysis   
4  [400:499]           4         400       499       None     None  analysis   
5  [500:599]           5         500       599       None     None  analysis   
6  [600:699]           6         600       699       None     None  analysis   
7  [700:799]           7         700       799       None     None  analysis   
8  [800:899]           8         800       899       None     None  analysis   
9  [900:999]           9         900       999       None     None  analysis   

           area_mean                                  ...       texture_mean  \
  kolmogorov_smirnov                                  ... kolmogorov_smirnov   
               value upper_threshold lower_threshold  ...    lower_threshold   
0              0.040        0.150643            None  ...               None   
1              0.089        0.150643            None  ...               None   
2              0.068        0.150643            None  ...               None   
3              0.117        0.150643            None  ...               None   
4              0.113        0.150643            None  ...               None   
5              0.055        0.150643            None  ...               None   
6              0.061        0.150643            None  ...               None   
7              0.060        0.150643            None  ...               None   
8              0.045        0.150643            None  ...               None   
9              0.089        0.150643            None  ...               None   

                 texture_se                                         \
         kolmogorov_smirnov                                          
   alert              value upper_threshold lower_threshold  alert   
0  False              0.066         0.09887            None  False   
1  False              0.061         0.09887            None  False   
2  False              0.085         0.09887            None  False   
3  False              0.054         0.09887            None  False   
4  False              0.061         0.09887            None  False   
5  False              0.036         0.09887            None  False   
6  False              0.068         0.09887            None  False   
7  False              0.060         0.09887            None  False   
8  False              0.073         0.09887            None  False   
9  False              0.064         0.09887            None  False   

       texture_worst                                         
  kolmogorov_smirnov                                         
               value upper_threshold lower_threshold  alert  
0              0.097        0.140661            None  False  
1              0.074        0.140661            None  False  
2              0.053        0.140661            None  False  
3              0.076        0.140661            None  False  
4              0.064        0.140661            None  False  
5              0.068        0.140661            None  False  
6              0.125        0.140661            None  False  
7              0.060        0.140661            None  False  
8              0.090        0.140661            None  False  
9              0.091        0.140661            None  False  

[10 rows x 127 columns]

##################################
# Visualizing univariate drift for baseline control
##################################
univariate_drift_analysis_visualization_p1 = plot_univariate_drift_summary(univariate_drift_analysis_p1, FEATURE_COLUMNS, "Baseline Control")

Univariate Drift Summary Table:

	feature	chunk_drift_count
0	radius_mean	0
1	texture_mean	0
2	perimeter_mean	0
3	area_mean	0
4	smoothness_mean	0
5	compactness_mean	0
6	concavity_mean	0
7	concave points_mean	0
8	symmetry_mean	0
9	fractal_dimension_mean	0
10	radius_se	0
11	texture_se	0
12	perimeter_se	0
13	area_se	0
14	smoothness_se	0
15	compactness_se	0
16	concavity_se	0
17	concave points_se	0
18	symmetry_se	0
19	fractal_dimension_se	0
20	radius_worst	0
21	texture_worst	0
22	perimeter_worst	0
23	area_worst	0
24	smoothness_worst	0
25	compactness_worst	0
26	concavity_worst	0
27	concave points_worst	0
28	symmetry_worst	0
29	fractal_dimension_worst	0

##################################
# Defining a function for fitting
# a CBPE estimator using the simulated baseline control and
# estimating CBPE performance per chunk for a given scenario
##################################
def estimate_chunk_cbpe_performance(reference_df, target_df, model_pipeline, feature_columns, target_col='diagnosis', label_map={'B':0, 'M':1}, chunk_col='__chunk'):
    """
    Fits CBPE Estimator on baseline data and estimate performance per chunk on scenario data.
    """

    # Preparing the reference data
    X_ref = reference_df[feature_columns]
    y_ref = reference_df[target_col].map(label_map)
    y_pred_ref, y_proba_ref = compute_preds_and_proba(model_pipeline, X_ref)

    ref_df = reference_df.copy()
    ref_df['y_true'] = y_ref
    ref_df['y_pred'] = y_pred_ref
    ref_df['y_pred_proba'] = y_proba_ref

    # Defining a chunker
    chunker = DefaultChunker()

    # Fitting CBPE on the reference data
    cbpe_estimator = CBPE(
        y_true='y_true',
        y_pred_proba='y_pred_proba',
        y_pred='y_pred',
        metrics=['roc_auc'],
        problem_type='classification_binary',
        chunker=chunker
    )
    cbpe_estimator.fit(ref_df)

    # Preparing the scenario data
    X_target = target_df[feature_columns]
    y_pred_target, y_proba_target = compute_preds_and_proba(model_pipeline, X_target)

    target_df_copy = target_df.copy()
    target_df_copy['y_pred'] = y_pred_target
    target_df_copy['y_pred_proba'] = y_proba_target

    # Estimating CBPE performance per chunk on the scenario data
    perf_results = cbpe_estimator.estimate(target_df_copy)

    chunk_cbpe_performance_summary = perf_results.to_df()

    print("Chunk CBPE Performance Summary Table:")
    display(chunk_cbpe_performance_summary)

    return chunk_cbpe_performance_summary
    

##################################
# Defining a function for visualizing
# CBPE performance for a given scenario
##################################
def plot_chunk_cbpe_performance(performance_df, baseline_name="Baseline", scenario_name="Scenario"):
    """
    Visualize CBPE-estimated ROC-AUC evolution per chunk for both reference and analysis periods,
    and summarize performance degradation alerts.
    """

    # Flattening the MultiIndex columns
    df = performance_df.copy()
    df.columns = ['_'.join(col).strip() if isinstance(col, tuple) else col for col in df.columns]
    
    # Ensure expected columns exist
    required_cols = [
        'chunk_chunk_index', 'chunk_period', 'roc_auc_value',
        'roc_auc_lower_confidence_boundary', 'roc_auc_upper_confidence_boundary', 'roc_auc_alert'
    ]
    missing = [c for c in required_cols if c not in df.columns]
    if missing:
        raise KeyError(f"Missing expected columns: {missing}")
    
    # Splitting results for reference and analysis scenarios
    df_ref = df[df['chunk_period'] == 'reference']
    df_analysis = df[df['chunk_period'] == 'analysis']

    # Using the reference confidence boundaries for both plots
    ref_bounds = df_ref[['chunk_chunk_index', 'roc_auc_lower_confidence_boundary', 'roc_auc_upper_confidence_boundary']]
    df_analysis = pd.merge(
        df_analysis.drop(columns=['roc_auc_lower_confidence_boundary', 'roc_auc_upper_confidence_boundary']),
        ref_bounds,
        on='chunk_chunk_index',
        how='left'
    )
    
    # Create a two-row plot
    fig, axes = plt.subplots(2, 1, figsize=(12, 7), sharex=True)
    sns.set_style("whitegrid")
    
    # Generating a helper function for consistent plotting
    def plot_cbpe_line(sub_df, ax, color, title):
        # Plotting the estimated performance
        sns.lineplot(
            data=sub_df,
            x='chunk_chunk_index',
            y='roc_auc_value',
            color=color,
            marker='o',
            ax=ax,
            label='Estimated ROC-AUC'
        )
    
        # Plotting the confidence region
        ax.fill_between(
            sub_df['chunk_chunk_index'],
            sub_df['roc_auc_lower_confidence_boundary'],
            sub_df['roc_auc_upper_confidence_boundary'],
            color=color,
            alpha=0.15
        )
    
        # Plotting the confidence boundary lines
        sns.lineplot(
            data=sub_df,
            x='chunk_chunk_index',
            y='roc_auc_upper_confidence_boundary',
            color='black',
            linestyle='-',
            ax=ax,
            label='Upper Confidence Bound'
        )
        sns.lineplot(
            data=sub_df,
            x='chunk_chunk_index',
            y='roc_auc_lower_confidence_boundary',
            color='red',
            linestyle='--',
            ax=ax,
            label='Lower Confidence Bound'
        )
    
        ax.set_title(title, fontsize=12)
        ax.set_xlabel("Chunk Index (Simulated Time)")
        ax.set_ylabel("CBPE-Estimated ROC-AUC")
        ax.set_ylim(0.8, 1.01)
        ax.set_yticks(np.arange(0.8, 1.01, 0.05))
        ax.set_xticks(range(10))
        ax.grid(True, alpha=0.3)
        ax.legend(loc='lower right', fontsize=8)
    
    # Plotting the reference CBPE ROC-AUC estimates
    plot_cbpe_line(df_ref, axes[0], color='blue', title=f"{baseline_name} (Reference Period)")
    
    # Plotting the scenario CBPE ROC-AUC estimates
    plot_cbpe_line(df_analysis, axes[1], color='orange', title=f"{scenario_name} (Analysis Period)")
    
    plt.tight_layout()
    plt.show()
    
    # # Formulating the summary table indicating the number of AUC-ROC alerts per chunk
    chunk_cbpe_performance_summary = (
        df.groupby(['chunk_chunk_index', 'chunk_period'])['roc_auc_alert']
        .sum()
        .reset_index()
        .rename(columns={'roc_auc_alert': 'cbpe_roc_auc_alert_count'})
    )
    
    print("Chunk CBPE Performance Summary Table:")
    display(chunk_cbpe_performance_summary)
    
    return chunk_cbpe_performance_summary

##################################
# Estimating CBPE performance for baseline control
##################################
chunk_cbpe_performance_analysis_p1 = estimate_chunk_cbpe_performance(p1, p1, boosted_cb_optimal, FEATURE_COLUMNS)

Chunk CBPE Performance Summary Table:

	chunk							roc_auc
	key	chunk_index	start_index	end_index	start_date	end_date	period	value	sampling_error	realized	upper_confidence_boundary	lower_confidence_boundary	upper_threshold	lower_threshold	alert
0	[0:99]	0	0	99	None	None	reference	0.994438	0.00367	0.9924	1.0	0.983427	1	0.976509	False
1	[100:199]	1	100	199	None	None	reference	0.997225	0.00367	0.9972	1.0	0.986213	1	0.976509	False
2	[200:299]	2	200	299	None	None	reference	0.997486	0.00367	1.0000	1.0	0.986475	1	0.976509	False
3	[300:399]	3	300	399	None	None	reference	0.995054	0.00367	0.9924	1.0	0.984043	1	0.976509	False
4	[400:499]	4	400	499	None	None	reference	0.996828	0.00367	0.9928	1.0	0.985817	1	0.976509	False
5	[500:599]	5	500	599	None	None	reference	0.995083	0.00367	0.9936	1.0	0.984072	1	0.976509	False
6	[600:699]	6	600	699	None	None	reference	0.996123	0.00367	0.9960	1.0	0.985111	1	0.976509	False
7	[700:799]	7	700	799	None	None	reference	0.995848	0.00367	0.9960	1.0	0.984836	1	0.976509	False
8	[800:899]	8	800	899	None	None	reference	0.991864	0.00367	0.9780	1.0	0.980853	1	0.976509	False
9	[900:999]	9	900	999	None	None	reference	0.994634	0.00367	0.9964	1.0	0.983623	1	0.976509	False
10	[0:99]	0	0	99	None	None	analysis	0.994438	0.00367	NaN	1.0	0.983427	1	0.976509	False
11	[100:199]	1	100	199	None	None	analysis	0.997225	0.00367	NaN	1.0	0.986213	1	0.976509	False
12	[200:299]	2	200	299	None	None	analysis	0.997486	0.00367	NaN	1.0	0.986475	1	0.976509	False
13	[300:399]	3	300	399	None	None	analysis	0.995054	0.00367	NaN	1.0	0.984043	1	0.976509	False
14	[400:499]	4	400	499	None	None	analysis	0.996828	0.00367	NaN	1.0	0.985817	1	0.976509	False
15	[500:599]	5	500	599	None	None	analysis	0.995083	0.00367	NaN	1.0	0.984072	1	0.976509	False
16	[600:699]	6	600	699	None	None	analysis	0.996123	0.00367	NaN	1.0	0.985111	1	0.976509	False
17	[700:799]	7	700	799	None	None	analysis	0.995848	0.00367	NaN	1.0	0.984836	1	0.976509	False
18	[800:899]	8	800	899	None	None	analysis	0.991864	0.00367	NaN	1.0	0.980853	1	0.976509	False
19	[900:999]	9	900	999	None	None	analysis	0.994634	0.00367	NaN	1.0	0.983623	1	0.976509	False

##################################
# Visualizing CBPE performance for baseline control
##################################
chunk_cbpe_performance_analysis_visualization_p1 = plot_chunk_cbpe_performance(chunk_cbpe_performance_analysis_p1, baseline_name="Baseline Control", scenario_name="Baseline Control")

Chunk CBPE Performance Summary Table:

	chunk_chunk_index	chunk_period	cbpe_roc_auc_alert_count
0	0	analysis	0
1	0	reference	0
2	1	analysis	0
3	1	reference	0
4	2	analysis	0
5	2	reference	0
6	3	analysis	0
7	3	reference	0
8	4	analysis	0
9	4	reference	0
10	5	analysis	0
11	5	reference	0
12	6	analysis	0
13	6	reference	0
14	7	analysis	0
15	7	reference	0
16	8	analysis	0
17	8	reference	0
18	9	analysis	0
19	9	reference	0

1.9.2 Simulated Covariate Drift

##################################
# Defining the covariate drift-specific parameters
# for the post-model deployment scenario simulation
##################################
COVARIATE_DRIFT_FEATURES = ['radius_mean','texture_mean','perimeter_mean','area_mean','smoothness_mean',
                            'compactness_mean','concavity_mean','concave points_mean','symmetry_mean','fractal_dimension_mean']
COVARIATE_DRIFT_DELTA = 0.5
COVARIATE_DRIFT_SCALE = 3.5
COVARIATE_DRIFT_RAMP = 15

##################################
# Defining a function for 
# simulating covariate drift
##################################
def simulate_P2_covariate_drift(df):
    # Creating a time-ordered synthetic stream of data chunks
    stream = make_stream_from_dataframe(df)
    # Computing standard deviations of selected features to scale drift magnitudes appropriately
    stds = df[COVARIATE_DRIFT_FEATURES].std()
    # Looping through each simulated chunk (time step)
    for chunk_idx in range(N_CHUNKS):
        # Computing the progression fraction (0 → 1) of the drift ramp over time
        frac = min(1, (chunk_idx+1)/COVARIATE_DRIFT_RAMP)
        # Applying a Boolean mask to isolate current chunk’s samples
        mask = stream['__chunk'] == chunk_idx
        # Applying drift to each feature selected for covariate drift
        for f in COVARIATE_DRIFT_FEATURES:
            # Applying an additive mean shift proportional to standard deviation and drift fraction
            add = COVARIATE_DRIFT_DELTA * stds[f] * frac
            # Applying a multiplicative scale shift proportional to drift progression
            scale = 1 + (COVARIATE_DRIFT_SCALE - 1) * frac
            # Apply both mean and scale shifts to current chunk’s feature values
            stream.loc[mask, f] = stream.loc[mask, f] * scale + add
    # Returning the modified data stream containing simulated covariate drift
    return stream

##################################
# Defining a function for 
# visualizing the boxplot comparison chart
# for both the simulated and baseline control
##################################
def plot_feature_boxplot_comparison(df_base, df_drift, features, scenario_name):
    """Chunk-based boxplots for selected features for Baseline vs Scenario."""
    # Resetting indices to avoid duplicate label issues
    df_base = df_base.reset_index(drop=True) 
    df_drift = df_drift.reset_index(drop=True)
    # Determining the number of features to plot
    n_features = len(features)
    # Creating a vertically stacked subplot layout (one plot per feature)
    fig, axes = plt.subplots(n_features, 1, figsize=(12, 3 * n_features), sharex=True)
    # Ensuring axes is iterable even if there’s only one feature
    if n_features == 1:
        axes = [axes]
    # Iterating through each feature and its corresponding subplot axis
    for ax, f in zip(axes, features):
        # Creating a boxplot showing the distribution of the feature across chunks
        combined_df = pd.concat([ df_base.assign(scenario='Baseline Control'), df_drift.assign(scenario=scenario_name) ], ignore_index=True).dropna(subset=[f, "__chunk"])
        sns.boxplot(
            data=combined_df,
            x="__chunk", y=f, hue="scenario", ax=ax, showfliers=False
        )
        y_min = combined_df[f].min() 
        y_max = combined_df[f].max() 
        y_extension = 0.2 * (y_max - y_min) 
        ax.set_ylim(y_min - y_extension, y_max + y_extension)
        ax.set_title(f"Chunk-wise {f}: {scenario_name} vs Baseline Control")
        ax.set_xlabel("Chunk Index (Simulated Time)")
        ax.set_ylabel(f)
        ax.legend(loc='upper left', bbox_to_anchor=(0, 1))
        ax.set_xticks(range(10))
    plt.tight_layout()
    plt.show()
    

##################################
# Defining a function for 
# visualizing the mean line comparison chart
# for both the simulated and baseline control
##################################
def plot_feature_mean_line(df_base, df_drift, features, scenario_name):
    """Plots per-feature mean values over chunks (one chart per feature) for Baseline vs Scenario."""
    # Computing the chunk-wise mean per feature for both datasets
    base_means = df_base.groupby('__chunk')[features].mean().assign(scenario='Baseline Control')
    drift_means = df_drift.groupby('__chunk')[features].mean().assign(scenario=scenario_name)
    combined = pd.concat([base_means, drift_means])
    melted = combined.reset_index().melt(
        id_vars=['__chunk', 'scenario'],
        var_name='feature',
        value_name='mean_value'
    )

    # Preparing the subplots (one row per feature)
    n_features = len(features)
    fig, axes = plt.subplots(n_features, 1, figsize=(12, 3 * n_features), sharex=True)
    if n_features == 1:
        axes = [axes]

    # Plotting the lineplots for each feature
    for ax, f in zip(axes, features):
        subset = melted[melted['feature'] == f]
        sns.lineplot(
            data=subset,
            x='__chunk',
            y='mean_value',
            hue='scenario',
            ax=ax
        )
        ax.set_title(f"Chunk-wise Mean of {f}: {scenario_name} vs Baseline", fontsize=11)
        ax.set_xlabel("Chunk Index")
        ax.set_ylabel("Mean Value")
        ax.grid(True, alpha=0.3)
        ax.set_xticks(range(10))
        ax.legend(loc='best')

    plt.tight_layout()
    plt.show()

##################################
# Simulating post-deployment data drift scenario 2 = covariate drift
##################################
p2 = simulate_P2_covariate_drift(breast_cancer_monitoring_baseline)

##################################
# Exploring the simulated covariate drift
##################################
display(p2)

	diagnosis	radius_mean	texture_mean	perimeter_mean	area_mean	smoothness_mean	compactness_mean	concavity_mean	concave points_mean	symmetry_mean	...	perimeter_worst	area_worst	smoothness_worst	compactness_worst	concavity_worst	concave points_worst	symmetry_worst	fractal_dimension_worst	__chunk	__timestamp
0	M	20.440009	29.953748	134.385875	1117.567389	0.117863	0.135572	0.198945	0.078271	0.153581	...	120.40	1021.0	0.1243	0.17930	0.280300	0.10990	0.1603	0.06818	0	0
1	M	26.098342	23.082082	179.069208	1772.067389	0.155196	0.324805	0.500178	0.213990	0.299181	...	206.80	2360.0	0.1701	0.69970	0.960800	0.29100	0.4055	0.09789	0	0
2	B	13.241676	17.377082	84.079208	466.567389	0.097399	0.053882	0.003847	0.004737	0.207831	...	82.08	492.7	0.1166	0.09794	0.005518	0.01667	0.2815	0.07418	0	0
3	B	14.408342	26.313748	92.012542	555.817389	0.096069	0.062539	0.022708	0.016018	0.181114	...	92.74	622.9	0.1256	0.18040	0.123000	0.06335	0.3100	0.08203	0	0
4	B	12.343342	23.303748	78.642542	405.550723	0.125329	0.071534	0.059073	0.037123	0.203631	...	73.68	402.8	0.1515	0.10260	0.118100	0.06736	0.2883	0.07748	0	0
...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...
995	B	38.580091	58.004150	247.465418	1724.740559	0.246825	0.203922	0.066099	0.063622	0.414339	...	98.27	715.5	0.1287	0.15130	0.062310	0.07963	0.2226	0.07617	9	9
996	B	37.726758	51.150816	244.638751	1638.340559	0.269385	0.304055	0.170712	0.113942	0.466872	...	99.43	701.9	0.1425	0.25660	0.193500	0.12840	0.2849	0.09031	9	9
997	B	36.046758	43.230816	236.372084	1502.340559	0.291625	0.357388	0.148925	0.095996	0.534339	...	96.09	630.5	0.1312	0.27760	0.189000	0.07283	0.3184	0.08183	9	9
998	B	24.092091	50.937483	152.265418	705.540559	0.291359	0.174642	0.027112	0.013062	0.586606	...	56.65	240.1	0.1347	0.07767	0.000000	0.00000	0.3142	0.08116	9	9
999	M	53.940091	68.324150	355.758751	3294.340559	0.275625	0.442455	0.705779	0.319462	0.597006	...	148.70	1589.0	0.1275	0.38610	0.567300	0.17320	0.3305	0.08465	9	9

1000 rows × 33 columns

##################################
# Visualizing baseline feature variability
# for the simulated covariate drift scenario
# and baseline control
##################################
plot_feature_boxplot_comparison(p1, p2, COVARIATE_DRIFT_FEATURES, "Covariate Drift")

##################################
# Visualizing baseline feature variability
# for the simulated covariate drift scenario
# and baseline control
##################################
plot_feature_mean_line(p1, p2, COVARIATE_DRIFT_FEATURES, "Covariate Drift")

##################################
# Inspecting class distribution
# for the simulated covariate drift scenario
# and baseline control
##################################
for feat in COVARIATE_DRIFT_FEATURES:
    fig, ax = plt.subplots(1, 2, figsize=(14, 3), sharey=True)
    combined_min = min(p1[feat].min(), p2[feat].min()) 
    combined_max = max(p1[feat].max(), p2[feat].max()) 
    y_margin = 0.05 * (combined_max - combined_min)
    y_min, y_max = combined_min - y_margin, combined_max + y_margin
    sns.boxplot(x="diagnosis", y=feat, data=p1, ax=ax[0], order=['M', 'B'])
    ax[0].set_title(f"{feat} by Label - Baseline Control")
    ax[0].set_ylim(y_min, y_max)
    sns.boxplot(x="diagnosis", y=feat, data=p2, ax=ax[1], order=['M', 'B'])
    ax[1].set_title(f"{feat} by Label - Covariate Drift")
    ax[1].set_ylim(y_min, y_max)
    plt.show() 

    

##################################
# Detecting univariate drift for covariate drift
##################################
univariate_drift_analysis_p2 = detect_univariate_drift(p1, p2, FEATURE_COLUMNS, "Covariate Drift")

Univariate drift visualization generated for Covariate Drift
       chunk                                                                  \
       chunk                                                                   
         key chunk_index start_index end_index start_date end_date    period   
0     [0:99]           0           0        99       None     None  analysis   
1  [100:199]           1         100       199       None     None  analysis   
2  [200:299]           2         200       299       None     None  analysis   
3  [300:399]           3         300       399       None     None  analysis   
4  [400:499]           4         400       499       None     None  analysis   
5  [500:599]           5         500       599       None     None  analysis   
6  [600:699]           6         600       699       None     None  analysis   
7  [700:799]           7         700       799       None     None  analysis   
8  [800:899]           8         800       899       None     None  analysis   
9  [900:999]           9         900       999       None     None  analysis   

           area_mean                                  ...       texture_mean  \
  kolmogorov_smirnov                                  ... kolmogorov_smirnov   
               value upper_threshold lower_threshold  ...    lower_threshold   
0              0.179        0.150643            None  ...               None   
1              0.321        0.150643            None  ...               None   
2              0.399        0.150643            None  ...               None   
3              0.527        0.150643            None  ...               None   
4              0.562        0.150643            None  ...               None   
5              0.594        0.150643            None  ...               None   
6              0.632        0.150643            None  ...               None   
7              0.660        0.150643            None  ...               None   
8              0.697        0.150643            None  ...               None   
9              0.712        0.150643            None  ...               None   

                texture_se                                         \
        kolmogorov_smirnov                                          
  alert              value upper_threshold lower_threshold  alert   
0  True              0.066         0.09887            None  False   
1  True              0.061         0.09887            None  False   
2  True              0.085         0.09887            None  False   
3  True              0.054         0.09887            None  False   
4  True              0.061         0.09887            None  False   
5  True              0.036         0.09887            None  False   
6  True              0.068         0.09887            None  False   
7  True              0.060         0.09887            None  False   
8  True              0.073         0.09887            None  False   
9  True              0.064         0.09887            None  False   

       texture_worst                                         
  kolmogorov_smirnov                                         
               value upper_threshold lower_threshold  alert  
0              0.097        0.140661            None  False  
1              0.074        0.140661            None  False  
2              0.053        0.140661            None  False  
3              0.076        0.140661            None  False  
4              0.064        0.140661            None  False  
5              0.068        0.140661            None  False  
6              0.125        0.140661            None  False  
7              0.060        0.140661            None  False  
8              0.090        0.140661            None  False  
9              0.091        0.140661            None  False  

[10 rows x 127 columns]

##################################
# Visualizing univariate drift for covariate drift
##################################
univariate_drift_analysis_visualization_p2 = plot_univariate_drift_summary(univariate_drift_analysis_p2, FEATURE_COLUMNS, "Covariate Drift")

Univariate Drift Summary Table:

	feature	chunk_drift_count
0	radius_mean	10
1	texture_mean	10
2	perimeter_mean	10
3	area_mean	10
4	smoothness_mean	10
5	compactness_mean	10
6	concavity_mean	10
7	concave points_mean	10
8	symmetry_mean	10
9	fractal_dimension_mean	10
10	radius_se	0
11	texture_se	0
12	perimeter_se	0
13	area_se	0
14	smoothness_se	0
15	compactness_se	0
16	concavity_se	0
17	concave points_se	0
18	symmetry_se	0
19	fractal_dimension_se	0
20	radius_worst	0
21	texture_worst	0
22	perimeter_worst	0
23	area_worst	0
24	smoothness_worst	0
25	compactness_worst	0
26	concavity_worst	0
27	concave points_worst	0
28	symmetry_worst	0
29	fractal_dimension_worst	0

##################################
# Estimating CBPE performance for covariate drift
##################################
chunk_cbpe_performance_analysis_p2 = estimate_chunk_cbpe_performance(p1, p2, boosted_cb_optimal, FEATURE_COLUMNS)

Chunk CBPE Performance Summary Table:

	chunk							roc_auc
	key	chunk_index	start_index	end_index	start_date	end_date	period	value	sampling_error	realized	upper_confidence_boundary	lower_confidence_boundary	upper_threshold	lower_threshold	alert
0	[0:99]	0	0	99	None	None	reference	0.994438	0.00367	0.9924	1.000000	0.983427	1	0.976509	False
1	[100:199]	1	100	199	None	None	reference	0.997225	0.00367	0.9972	1.000000	0.986213	1	0.976509	False
2	[200:299]	2	200	299	None	None	reference	0.997486	0.00367	1.0000	1.000000	0.986475	1	0.976509	False
3	[300:399]	3	300	399	None	None	reference	0.995054	0.00367	0.9924	1.000000	0.984043	1	0.976509	False
4	[400:499]	4	400	499	None	None	reference	0.996828	0.00367	0.9928	1.000000	0.985817	1	0.976509	False
5	[500:599]	5	500	599	None	None	reference	0.995083	0.00367	0.9936	1.000000	0.984072	1	0.976509	False
6	[600:699]	6	600	699	None	None	reference	0.996123	0.00367	0.9960	1.000000	0.985111	1	0.976509	False
7	[700:799]	7	700	799	None	None	reference	0.995848	0.00367	0.9960	1.000000	0.984836	1	0.976509	False
8	[800:899]	8	800	899	None	None	reference	0.991864	0.00367	0.9780	1.000000	0.980853	1	0.976509	False
9	[900:999]	9	900	999	None	None	reference	0.994634	0.00367	0.9964	1.000000	0.983623	1	0.976509	False
10	[0:99]	0	0	99	None	None	analysis	0.993605	0.00367	NaN	1.000000	0.982594	1	0.976509	False
11	[100:199]	1	100	199	None	None	analysis	0.995865	0.00367	NaN	1.000000	0.984854	1	0.976509	False
12	[200:299]	2	200	299	None	None	analysis	0.973295	0.00367	NaN	0.984306	0.962283	1	0.976509	True
13	[300:399]	3	300	399	None	None	analysis	0.980802	0.00367	NaN	0.991813	0.969790	1	0.976509	False
14	[400:499]	4	400	499	None	None	analysis	0.974865	0.00367	NaN	0.985877	0.963854	1	0.976509	True
15	[500:599]	5	500	599	None	None	analysis	0.984459	0.00367	NaN	0.995471	0.973448	1	0.976509	False
16	[600:699]	6	600	699	None	None	analysis	0.951432	0.00367	NaN	0.962443	0.940420	1	0.976509	True
17	[700:799]	7	700	799	None	None	analysis	0.936062	0.00367	NaN	0.947074	0.925051	1	0.976509	True
18	[800:899]	8	800	899	None	None	analysis	0.842986	0.00367	NaN	0.853997	0.831974	1	0.976509	True
19	[900:999]	9	900	999	None	None	analysis	0.804781	0.00367	NaN	0.815793	0.793770	1	0.976509	True

##################################
# Visualizing CBPE performance for covariate drift
##################################
chunk_cbpe_performance_analysis_visualization_p2 = plot_chunk_cbpe_performance(chunk_cbpe_performance_analysis_p2, baseline_name="Baseline Control", scenario_name="Covariate Drift")

Chunk CBPE Performance Summary Table:

	chunk_chunk_index	chunk_period	cbpe_roc_auc_alert_count
0	0	analysis	0
1	0	reference	0
2	1	analysis	0
3	1	reference	0
4	2	analysis	1
5	2	reference	0
6	3	analysis	0
7	3	reference	0
8	4	analysis	1
9	4	reference	0
10	5	analysis	0
11	5	reference	0
12	6	analysis	1
13	6	reference	0
14	7	analysis	1
15	7	reference	0
16	8	analysis	1
17	8	reference	0
18	9	analysis	1
19	9	reference	0

1.9.3 Simulated Prior Shift

##################################
# Defining the prior-shift parameters
# for the post-model deployment scenario simulation
##################################
PRIOR_SHIFT_START_P = 0.30
PRIOR_SHIFT_END_P = 0.80
PRIOR_SHIFT_RAMP = 5

##################################
# Defining a function for 
# simulating prior shift
##################################
def simulate_P3_prior_shift(df):
    # Initialiing a random number generator for reproducibility
    rng = np.random.RandomState(RANDOM_STATE)
    # Separating the dataset into positive (M) and negative (B) subsets
    df_pos = df[df[TARGET_COL].map(LABEL_MAP)==1]
    df_neg = df[df[TARGET_COL].map(LABEL_MAP)==0]
    # Creating an empty list to collect chunked DataFrames
    chunks = []
    # Iterating over each simulated monitoring chunk
    for c in range(N_CHUNKS):
        # Calculating the current progression fraction (0 → 1)
        frac = min(1, (c+1)/PRIOR_SHIFT_RAMP)
        # Gradually changing the class prevalence (probability of positives)
        p = PRIOR_SHIFT_START_P + (PRIOR_SHIFT_END_P - PRIOR_SHIFT_START_P) * frac
        # Determining the number of positive and negative samples in the particular chunk
        n_pos = int(CHUNK_SIZE * p)
        n_neg = CHUNK_SIZE - n_pos
        # Sampling from positive and negative pools with replacement
        pos = df_pos.sample(n=n_pos, replace=True, random_state=rng.randint(0,2**31 -1))
        neg = df_neg.sample(n=n_neg, replace=True, random_state=rng.randint(0,2**31 -1))
        # Combining and shuffling the sampled data to avoid order bias
        chunk = pd.concat([pos, neg]).sample(frac=1, random_state=rng.randint(0,2**31 -1))
        # Assigning synthetic time and chunk identifiers
        chunk['__chunk']=c; 
        chunk['__timestamp']=c
        # Store the chunk in the list
        chunks.append(chunk)
    # Concatenating all chunks into a single DataFrame for analysis    
    return pd.concat(chunks, ignore_index=True)

##################################
# Defining a function for 
# plotting class proportion ('M' vs 'B') across chunks
# for both the simulated and baseline control
##################################
def plot_class_proportion(df_base, df_shift, scenario_name):
    def prop(df):
        return df.groupby('__chunk')['diagnosis'].value_counts(normalize=True).unstack().fillna(0)
    base_prop = prop(df_base)
    shift_prop = prop(df_shift)
    fig, ax = plt.subplots(figsize=(14, 3))
    sns.lineplot(data=base_prop['M'], label='Baseline M', ax=ax)
    sns.lineplot(data=shift_prop['M'], label=f'{scenario_name} M', ax=ax)
    ax.set_title(f"Proportion of Malignant (M) per Chunk: {scenario_name} vs Baseline Control")
    ax.set_xlabel("Chunk Index")
    ax.set_ylabel("Proportion of 'M'")
    ax.set_ylim(-0.1, 1)
    ax.set_xticks(range(10))
    ax.legend()
    plt.show()
    

##################################
# Simulating post-deployment data drift scenario 3 = prior shift
##################################
p3 = simulate_P3_prior_shift(breast_cancer_monitoring_baseline)

##################################
# Exploring the simulated prior shift
##################################
display(p3)

	diagnosis	radius_mean	texture_mean	perimeter_mean	area_mean	smoothness_mean	compactness_mean	concavity_mean	concave points_mean	symmetry_mean	...	perimeter_worst	area_worst	smoothness_worst	compactness_worst	concavity_worst	concave points_worst	symmetry_worst	fractal_dimension_worst	__chunk	__timestamp
0	B	10.80	21.98	68.79	359.9	0.08801	0.05743	0.036140	0.014040	0.2016	...	83.69	489.5	0.13030	0.16960	0.19270	0.07485	0.2965	0.07662	0	0
1	M	22.27	19.67	152.80	1509.0	0.13260	0.27680	0.426400	0.182300	0.2556	...	206.80	2360.0	0.17010	0.69970	0.96080	0.29100	0.4055	0.09789	0	0
2	B	9.72	18.22	60.73	288.1	0.06950	0.02344	0.000000	0.000000	0.1653	...	62.25	303.8	0.07117	0.02729	0.00000	0.00000	0.1909	0.06559	0	0
3	B	11.51	23.93	74.52	403.5	0.09261	0.10210	0.111200	0.041050	0.1388	...	82.28	474.2	0.12980	0.25170	0.36300	0.09653	0.2112	0.08732	0	0
4	B	13.50	12.71	85.69	566.2	0.07376	0.03614	0.002758	0.004419	0.1365	...	95.48	698.7	0.09023	0.05836	0.01379	0.02210	0.2267	0.06192	0	0
...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...
995	M	17.68	20.74	117.40	963.7	0.11150	0.16650	0.185500	0.105400	0.1971	...	132.90	1302.0	0.14180	0.34980	0.35830	0.15150	0.2463	0.07738	9	9
996	B	12.96	18.29	84.18	525.2	0.07351	0.07899	0.040570	0.018830	0.1874	...	96.31	621.9	0.09329	0.23180	0.16040	0.06608	0.3207	0.07247	9	9
997	M	18.66	17.12	121.40	1077.0	0.10540	0.11000	0.145700	0.086650	0.1966	...	145.40	1549.0	0.15030	0.22910	0.32720	0.16740	0.2894	0.08456	9	9
998	M	18.25	19.98	119.60	1040.0	0.09463	0.10900	0.112700	0.074000	0.1794	...	153.20	1606.0	0.14420	0.25760	0.37840	0.19320	0.3063	0.08368	9	9
999	M	19.79	25.12	130.40	1192.0	0.10150	0.15890	0.254500	0.114900	0.2202	...	148.70	1589.0	0.12750	0.38610	0.56730	0.17320	0.3305	0.08465	9	9

1000 rows × 33 columns

##################################
# Inspecting class balance stability
# for the simulated prior shift scenario
# and baseline control
##################################
plot_class_proportion(p1, p3, "Prior Shift")

##################################
# Visualizing baseline feature variability
# for the simulated prior shift scenario
# and baseline control
##################################
plot_feature_boxplot_comparison(p1, p3, FEATURE_COLUMNS, "Prior Shift")

##################################
# Inspecting class distribution
# for the simulated prior shift scenario
# and baseline control
##################################
for feat in FEATURE_COLUMNS:
    fig, ax = plt.subplots(1, 2, figsize=(14, 3), sharey=True)
    combined_min = min(p1[feat].min(), p3[feat].min()) 
    combined_max = max(p1[feat].max(), p3[feat].max()) 
    y_margin = 0.05 * (combined_max - combined_min)
    y_min, y_max = combined_min - y_margin, combined_max + y_margin
    sns.boxplot(x="diagnosis", y=feat, data=p1, ax=ax[0], order=['M', 'B'])
    ax[0].set_title(f"{feat} by Label - Baseline Control")
    ax[0].set_ylim(y_min, y_max)
    sns.boxplot(x="diagnosis", y=feat, data=p3, ax=ax[1], order=['M', 'B'])
    ax[1].set_title(f"{feat} by Label - Prior Shift")
    ax[1].set_ylim(y_min, y_max)
    plt.show()
    

##################################
# Detecting univariate drift for prior shift
##################################
univariate_drift_analysis_p3 = detect_univariate_drift(p1, p3, FEATURE_COLUMNS, "Prior Shift")

Univariate drift visualization generated for Prior Shift
       chunk                                                                  \
       chunk                                                                   
         key chunk_index start_index end_index start_date end_date    period   
0     [0:99]           0           0        99       None     None  analysis   
1  [100:199]           1         100       199       None     None  analysis   
2  [200:299]           2         200       299       None     None  analysis   
3  [300:399]           3         300       399       None     None  analysis   
4  [400:499]           4         400       499       None     None  analysis   
5  [500:599]           5         500       599       None     None  analysis   
6  [600:699]           6         600       699       None     None  analysis   
7  [700:799]           7         700       799       None     None  analysis   
8  [800:899]           8         800       899       None     None  analysis   
9  [900:999]           9         900       999       None     None  analysis   

           area_mean                                  ...       texture_mean  \
  kolmogorov_smirnov                                  ... kolmogorov_smirnov   
               value upper_threshold lower_threshold  ...    lower_threshold   
0              0.102        0.150643            None  ...               None   
1              0.089        0.150643            None  ...               None   
2              0.168        0.150643            None  ...               None   
3              0.232        0.150643            None  ...               None   
4              0.203        0.150643            None  ...               None   
5              0.243        0.150643            None  ...               None   
6              0.237        0.150643            None  ...               None   
7              0.232        0.150643            None  ...               None   
8              0.289        0.150643            None  ...               None   
9              0.347        0.150643            None  ...               None   

                 texture_se                                         \
         kolmogorov_smirnov                                          
   alert              value upper_threshold lower_threshold  alert   
0  False              0.083         0.09887            None  False   
1  False              0.061         0.09887            None  False   
2  False              0.077         0.09887            None  False   
3  False              0.062         0.09887            None  False   
4   True              0.054         0.09887            None  False   
5   True              0.067         0.09887            None  False   
6  False              0.071         0.09887            None  False   
7   True              0.080         0.09887            None  False   
8   True              0.101         0.09887            None   True   
9   True              0.054         0.09887            None  False   

       texture_worst                                         
  kolmogorov_smirnov                                         
               value upper_threshold lower_threshold  alert  
0              0.121        0.140661            None  False  
1              0.074        0.140661            None  False  
2              0.091        0.140661            None  False  
3              0.114        0.140661            None  False  
4              0.174        0.140661            None   True  
5              0.221        0.140661            None   True  
6              0.131        0.140661            None  False  
7              0.130        0.140661            None  False  
8              0.214        0.140661            None   True  
9              0.180        0.140661            None   True  

[10 rows x 127 columns]

##################################
# Visualizing univariate drift for prior shift
##################################
univariate_drift_analysis_visualization_p3 = plot_univariate_drift_summary(univariate_drift_analysis_p3, FEATURE_COLUMNS, "Prior Shift")

Univariate Drift Summary Table:

	feature	chunk_drift_count
0	radius_mean	8
1	texture_mean	5
2	perimeter_mean	8
3	area_mean	8
4	smoothness_mean	5
5	compactness_mean	7
6	concavity_mean	8
7	concave points_mean	8
8	symmetry_mean	3
9	fractal_dimension_mean	0
10	radius_se	7
11	texture_se	1
12	perimeter_se	7
13	area_se	7
14	smoothness_se	0
15	compactness_se	2
16	concavity_se	5
17	concave points_se	6
18	symmetry_se	1
19	fractal_dimension_se	0
20	radius_worst	8
21	texture_worst	4
22	perimeter_worst	8
23	area_worst	8
24	smoothness_worst	7
25	compactness_worst	7
26	concavity_worst	7
27	concave points_worst	7
28	symmetry_worst	1
29	fractal_dimension_worst	2

##################################
# Estimating CBPE performance for prior shift
##################################
chunk_cbpe_performance_analysis_p3 = estimate_chunk_cbpe_performance(p1, p3, boosted_cb_optimal, FEATURE_COLUMNS)

Chunk CBPE Performance Summary Table:

	chunk							roc_auc
	key	chunk_index	start_index	end_index	start_date	end_date	period	value	sampling_error	realized	upper_confidence_boundary	lower_confidence_boundary	upper_threshold	lower_threshold	alert
0	[0:99]	0	0	99	None	None	reference	0.994438	0.00367	0.9924	1.0	0.983427	1	0.976509	False
1	[100:199]	1	100	199	None	None	reference	0.997225	0.00367	0.9972	1.0	0.986213	1	0.976509	False
2	[200:299]	2	200	299	None	None	reference	0.997486	0.00367	1.0000	1.0	0.986475	1	0.976509	False
3	[300:399]	3	300	399	None	None	reference	0.995054	0.00367	0.9924	1.0	0.984043	1	0.976509	False
4	[400:499]	4	400	499	None	None	reference	0.996828	0.00367	0.9928	1.0	0.985817	1	0.976509	False
5	[500:599]	5	500	599	None	None	reference	0.995083	0.00367	0.9936	1.0	0.984072	1	0.976509	False
6	[600:699]	6	600	699	None	None	reference	0.996123	0.00367	0.9960	1.0	0.985111	1	0.976509	False
7	[700:799]	7	700	799	None	None	reference	0.995848	0.00367	0.9960	1.0	0.984836	1	0.976509	False
8	[800:899]	8	800	899	None	None	reference	0.991864	0.00367	0.9780	1.0	0.980853	1	0.976509	False
9	[900:999]	9	900	999	None	None	reference	0.994634	0.00367	0.9964	1.0	0.983623	1	0.976509	False
10	[0:99]	0	0	99	None	None	analysis	0.993098	0.00367	NaN	1.0	0.982087	1	0.976509	False
11	[100:199]	1	100	199	None	None	analysis	0.997225	0.00367	NaN	1.0	0.986213	1	0.976509	False
12	[200:299]	2	200	299	None	None	analysis	0.997405	0.00367	NaN	1.0	0.986394	1	0.976509	False
13	[300:399]	3	300	399	None	None	analysis	0.996471	0.00367	NaN	1.0	0.985460	1	0.976509	False
14	[400:499]	4	400	499	None	None	analysis	0.996010	0.00367	NaN	1.0	0.984998	1	0.976509	False
15	[500:599]	5	500	599	None	None	analysis	0.996252	0.00367	NaN	1.0	0.985240	1	0.976509	False
16	[600:699]	6	600	699	None	None	analysis	0.992699	0.00367	NaN	1.0	0.981688	1	0.976509	False
17	[700:799]	7	700	799	None	None	analysis	0.992849	0.00367	NaN	1.0	0.981838	1	0.976509	False
18	[800:899]	8	800	899	None	None	analysis	0.992422	0.00367	NaN	1.0	0.981410	1	0.976509	False
19	[900:999]	9	900	999	None	None	analysis	0.993719	0.00367	NaN	1.0	0.982708	1	0.976509	False

##################################
# Visualizing CBPE performance for prior shift
##################################
chunk_cbpe_performance_analysis_visualization_p3 = plot_chunk_cbpe_performance(chunk_cbpe_performance_analysis_p3, baseline_name="Baseline Control", scenario_name="Prior Shift")

Chunk CBPE Performance Summary Table:

	chunk_chunk_index	chunk_period	cbpe_roc_auc_alert_count
0	0	analysis	0
1	0	reference	0
2	1	analysis	0
3	1	reference	0
4	2	analysis	0
5	2	reference	0
6	3	analysis	0
7	3	reference	0
8	4	analysis	0
9	4	reference	0
10	5	analysis	0
11	5	reference	0
12	6	analysis	0
13	6	reference	0
14	7	analysis	0
15	7	reference	0
16	8	analysis	0
17	8	reference	0
18	9	analysis	0
19	9	reference	0

1.9.4 Simulated Concept Drift

##################################
# Defining the concept drift-specific parameters
# for the post-model deployment scenario simulation
##################################
CONCEPT_DRIFT_SLICE_FEATURES = ['radius_mean','texture_mean','perimeter_mean','area_mean','smoothness_mean',
'compactness_se','concavity_se','concave points_se','symmetry_se','fractal_dimension_se',
'radius_worst','perimeter_worst', 'smoothness_worst','concavity_worst','symmetry_worst']
CONCEPT_DRIFT_SLICE_THRESHOLD_QUANTILE = 0.75
CONCEPT_DRIFT_FLIP_FRACTION = 1.0
CONCEPT_DRIFT_RAMP = 10

##################################
# Defining a function for 
# simulating concept drift
##################################
def simulate_P4_concept_drift(df):
    # Initializing a random number generator for reproducibility
    rng = np.random.RandomState(RANDOM_STATE)
    # Creating a time-ordered synthetic stream of data chunks
    stream = make_stream_from_dataframe(df)
    # Iterating through each feature defined to induce localized concept drift
    for feat in CONCEPT_DRIFT_SLICE_FEATURES:
        # Determining a threshold (quantile-based) to define the region affected by concept drift
        thr = df[feat].quantile(CONCEPT_DRIFT_SLICE_THRESHOLD_QUANTILE)
        # Looping through each synthetic chunk (simulated monitoring time)
        for c in range(N_CHUNKS):
            # Computing progression of concept drift (0 → 1) across ramp duration
            frac = min(1.0, (c+1)/CONCEPT_DRIFT_RAMP)
            # Identifying data points within the current chunk and above the feature threshold
            mask = (stream['__chunk']==c) & (stream[feat]>=thr)
            # Extracting indices of samples eligible for label flipping
            idxs = stream[mask].index
            # Computing number of samples to flip based on drift fraction and configured flip rate
            n_flip = int(len(idxs) * CONCEPT_DRIFT_FLIP_FRACTION * frac)
            # Performing label flipping only if there are samples to modify
            if n_flip>0:
                flip = rng.choice(idxs, n_flip, replace=False)
                # Swapping labels: 'B' becomes 'M', and 'M' becomes 'B'
                stream.loc[flip, TARGET_COL] = stream.loc[flip, TARGET_COL].map({'B':'M','M':'B'})
    # Returning the modified data stream containing simulated concept drift
    return stream

##################################
# Simulating post-deployment data drift scenario 4 = concept drift
##################################
p4 = simulate_P4_concept_drift(breast_cancer_monitoring_baseline)

##################################
# Exploring the simulated concept drift
##################################
display(p4)

	diagnosis	radius_mean	texture_mean	perimeter_mean	area_mean	smoothness_mean	compactness_mean	concavity_mean	concave points_mean	symmetry_mean	...	perimeter_worst	area_worst	smoothness_worst	compactness_worst	concavity_worst	concave points_worst	symmetry_worst	fractal_dimension_worst	__chunk	__timestamp
0	B	17.420	25.56	114.50	948.0	0.10060	0.11460	0.168200	0.065970	0.1308	...	120.40	1021.0	0.1243	0.17930	0.280300	0.10990	0.1603	0.06818	0	0
1	B	22.270	19.67	152.80	1509.0	0.13260	0.27680	0.426400	0.182300	0.2556	...	206.80	2360.0	0.1701	0.69970	0.960800	0.29100	0.4055	0.09789	0	0
2	B	11.250	14.78	71.38	390.0	0.08306	0.04458	0.000974	0.002941	0.1773	...	82.08	492.7	0.1166	0.09794	0.005518	0.01667	0.2815	0.07418	0	0
3	B	12.250	22.44	78.18	466.5	0.08192	0.05200	0.017140	0.012610	0.1544	...	92.74	622.9	0.1256	0.18040	0.123000	0.06335	0.3100	0.08203	0	0
4	B	10.480	19.86	66.72	337.7	0.10700	0.05971	0.048310	0.030700	0.1737	...	73.68	402.8	0.1515	0.10260	0.118100	0.06736	0.2883	0.07748	0	0
...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...
995	B	14.030	21.25	89.79	603.4	0.09070	0.06945	0.014620	0.018960	0.1517	...	98.27	715.5	0.1287	0.15130	0.062310	0.07963	0.2226	0.07617	9	9
996	B	13.710	18.68	88.73	571.0	0.09916	0.10700	0.053850	0.037830	0.1714	...	99.43	701.9	0.1425	0.25660	0.193500	0.12840	0.2849	0.09031	9	9
997	B	13.080	15.71	85.63	520.0	0.10750	0.12700	0.045680	0.031100	0.1967	...	96.09	630.5	0.1312	0.27760	0.189000	0.07283	0.3184	0.08183	9	9
998	M	8.597	18.60	54.09	221.2	0.10740	0.05847	0.000000	0.000000	0.2163	...	56.65	240.1	0.1347	0.07767	0.000000	0.00000	0.3142	0.08116	9	9
999	B	19.790	25.12	130.40	1192.0	0.10150	0.15890	0.254500	0.114900	0.2202	...	148.70	1589.0	0.1275	0.38610	0.567300	0.17320	0.3305	0.08465	9	9

1000 rows × 33 columns

##################################
# Inspecting class balance stability
# for the simulated concept drift scenario
# and baseline control
##################################
plot_class_proportion(p1, p4, "Concept Drift")

##################################
# Visualizing baseline feature variability
# for the simulated concept drift scenario
# and baseline control
##################################
plot_feature_boxplot_comparison(p1, p4, CONCEPT_DRIFT_SLICE_FEATURES, "Concept Drift")

##################################
# Inspecting class distribution
# for the simulated concept drift scenario
# and baseline control
##################################
for feat in CONCEPT_DRIFT_SLICE_FEATURES:
    fig, ax = plt.subplots(1, 2, figsize=(14, 3), sharey=True)
    combined_min = min(p1[feat].min(), p4[feat].min()) 
    combined_max = max(p1[feat].max(), p4[feat].max()) 
    y_margin = 0.05 * (combined_max - combined_min)
    y_min, y_max = combined_min - y_margin, combined_max + y_margin
    sns.boxplot(x="diagnosis", y=feat, data=p1, ax=ax[0], order=['M', 'B'])
    ax[0].set_title(f"{feat} by Label - Baseline Control")
    ax[0].set_ylim(y_min, y_max)
    sns.boxplot(x="diagnosis", y=feat, data=p4, ax=ax[1], order=['M', 'B'])
    ax[1].set_title(f"{feat} by Label - Concept Drift")
    ax[1].set_ylim(y_min, y_max)
    plt.show()
    

##################################
# Detecting univariate drift for concept drift
##################################
univariate_drift_analysis_p4 = detect_univariate_drift(p1, p4, FEATURE_COLUMNS, "Concept Drift")

Univariate drift visualization generated for Concept Drift
       chunk                                                                  \
       chunk                                                                   
         key chunk_index start_index end_index start_date end_date    period   
0     [0:99]           0           0        99       None     None  analysis   
1  [100:199]           1         100       199       None     None  analysis   
2  [200:299]           2         200       299       None     None  analysis   
3  [300:399]           3         300       399       None     None  analysis   
4  [400:499]           4         400       499       None     None  analysis   
5  [500:599]           5         500       599       None     None  analysis   
6  [600:699]           6         600       699       None     None  analysis   
7  [700:799]           7         700       799       None     None  analysis   
8  [800:899]           8         800       899       None     None  analysis   
9  [900:999]           9         900       999       None     None  analysis   

           area_mean                                  ...       texture_mean  \
  kolmogorov_smirnov                                  ... kolmogorov_smirnov   
               value upper_threshold lower_threshold  ...    lower_threshold   
0              0.040        0.150643            None  ...               None   
1              0.089        0.150643            None  ...               None   
2              0.068        0.150643            None  ...               None   
3              0.117        0.150643            None  ...               None   
4              0.113        0.150643            None  ...               None   
5              0.055        0.150643            None  ...               None   
6              0.061        0.150643            None  ...               None   
7              0.060        0.150643            None  ...               None   
8              0.045        0.150643            None  ...               None   
9              0.089        0.150643            None  ...               None   

                 texture_se                                         \
         kolmogorov_smirnov                                          
   alert              value upper_threshold lower_threshold  alert   
0  False              0.066         0.09887            None  False   
1  False              0.061         0.09887            None  False   
2  False              0.085         0.09887            None  False   
3  False              0.054         0.09887            None  False   
4  False              0.061         0.09887            None  False   
5  False              0.036         0.09887            None  False   
6  False              0.068         0.09887            None  False   
7  False              0.060         0.09887            None  False   
8  False              0.073         0.09887            None  False   
9  False              0.064         0.09887            None  False   

       texture_worst                                         
  kolmogorov_smirnov                                         
               value upper_threshold lower_threshold  alert  
0              0.097        0.140661            None  False  
1              0.074        0.140661            None  False  
2              0.053        0.140661            None  False  
3              0.076        0.140661            None  False  
4              0.064        0.140661            None  False  
5              0.068        0.140661            None  False  
6              0.125        0.140661            None  False  
7              0.060        0.140661            None  False  
8              0.090        0.140661            None  False  
9              0.091        0.140661            None  False  

[10 rows x 127 columns]

##################################
# Visualizing univariate drift for concept drift
##################################
univariate_drift_analysis_visualization_p4 = plot_univariate_drift_summary(univariate_drift_analysis_p4, FEATURE_COLUMNS, "Concept Drift")

Univariate Drift Summary Table:

	feature	chunk_drift_count
0	radius_mean	0
1	texture_mean	0
2	perimeter_mean	0
3	area_mean	0
4	smoothness_mean	0
5	compactness_mean	0
6	concavity_mean	0
7	concave points_mean	0
8	symmetry_mean	0
9	fractal_dimension_mean	0
10	radius_se	0
11	texture_se	0
12	perimeter_se	0
13	area_se	0
14	smoothness_se	0
15	compactness_se	0
16	concavity_se	0
17	concave points_se	0
18	symmetry_se	0
19	fractal_dimension_se	0
20	radius_worst	0
21	texture_worst	0
22	perimeter_worst	0
23	area_worst	0
24	smoothness_worst	0
25	compactness_worst	0
26	concavity_worst	0
27	concave points_worst	0
28	symmetry_worst	0
29	fractal_dimension_worst	0

##################################
# Estimating CBPE performance for concept drift
##################################
chunk_cbpe_performance_analysis_p4 = estimate_chunk_cbpe_performance(p1, p4, boosted_cb_optimal, FEATURE_COLUMNS)

Chunk CBPE Performance Summary Table:

	chunk							roc_auc
	key	chunk_index	start_index	end_index	start_date	end_date	period	value	sampling_error	realized	upper_confidence_boundary	lower_confidence_boundary	upper_threshold	lower_threshold	alert
0	[0:99]	0	0	99	None	None	reference	0.994438	0.00367	0.9924	1.0	0.983427	1	0.976509	False
1	[100:199]	1	100	199	None	None	reference	0.997225	0.00367	0.9972	1.0	0.986213	1	0.976509	False
2	[200:299]	2	200	299	None	None	reference	0.997486	0.00367	1.0000	1.0	0.986475	1	0.976509	False
3	[300:399]	3	300	399	None	None	reference	0.995054	0.00367	0.9924	1.0	0.984043	1	0.976509	False
4	[400:499]	4	400	499	None	None	reference	0.996828	0.00367	0.9928	1.0	0.985817	1	0.976509	False
5	[500:599]	5	500	599	None	None	reference	0.995083	0.00367	0.9936	1.0	0.984072	1	0.976509	False
6	[600:699]	6	600	699	None	None	reference	0.996123	0.00367	0.9960	1.0	0.985111	1	0.976509	False
7	[700:799]	7	700	799	None	None	reference	0.995848	0.00367	0.9960	1.0	0.984836	1	0.976509	False
8	[800:899]	8	800	899	None	None	reference	0.991864	0.00367	0.9780	1.0	0.980853	1	0.976509	False
9	[900:999]	9	900	999	None	None	reference	0.994634	0.00367	0.9964	1.0	0.983623	1	0.976509	False
10	[0:99]	0	0	99	None	None	analysis	0.994438	0.00367	NaN	1.0	0.983427	1	0.976509	False
11	[100:199]	1	100	199	None	None	analysis	0.997225	0.00367	NaN	1.0	0.986213	1	0.976509	False
12	[200:299]	2	200	299	None	None	analysis	0.997486	0.00367	NaN	1.0	0.986475	1	0.976509	False
13	[300:399]	3	300	399	None	None	analysis	0.995054	0.00367	NaN	1.0	0.984043	1	0.976509	False
14	[400:499]	4	400	499	None	None	analysis	0.996828	0.00367	NaN	1.0	0.985817	1	0.976509	False
15	[500:599]	5	500	599	None	None	analysis	0.995083	0.00367	NaN	1.0	0.984072	1	0.976509	False
16	[600:699]	6	600	699	None	None	analysis	0.996123	0.00367	NaN	1.0	0.985111	1	0.976509	False
17	[700:799]	7	700	799	None	None	analysis	0.995848	0.00367	NaN	1.0	0.984836	1	0.976509	False
18	[800:899]	8	800	899	None	None	analysis	0.991864	0.00367	NaN	1.0	0.980853	1	0.976509	False
19	[900:999]	9	900	999	None	None	analysis	0.994634	0.00367	NaN	1.0	0.983623	1	0.976509	False

##################################
# Visualizing CBPE performance for concept drift
##################################
chunk_cbpe_performance_analysis_visualization_p4 = plot_chunk_cbpe_performance(chunk_cbpe_performance_analysis_p4, baseline_name="Baseline Control", scenario_name="Concept Drift")

Chunk CBPE Performance Summary Table:

	chunk_chunk_index	chunk_period	cbpe_roc_auc_alert_count
0	0	analysis	0
1	0	reference	0
2	1	analysis	0
3	1	reference	0
4	2	analysis	0
5	2	reference	0
6	3	analysis	0
7	3	reference	0
8	4	analysis	0
9	4	reference	0
10	5	analysis	0
11	5	reference	0
12	6	analysis	0
13	6	reference	0
14	7	analysis	0
15	7	reference	0
16	8	analysis	0
17	8	reference	0
18	9	analysis	0
19	9	reference	0

1.9.5 Simulated Missingness Spike

##################################
# Defining the missingness spike-specific parameters
# for the post-model deployment scenario simulation
##################################
MCAR_FEATURES = ['radius_mean','texture_mean','perimeter_mean','area_mean','smoothness_mean', 'compactness_mean','concavity_mean']
MAR_FEATURES = ['compactness_mean','concavity_mean','concave points_mean','symmetry_mean','fractal_dimension_mean']
MISSINGNESS_SPIKE_FEATURES = list(dict.fromkeys(MCAR_FEATURES + MAR_FEATURES))
MISSINGNESS_SPIKE_INTENSITY = 0.8
MISSINGNESS_SPIKE_LENGTH = 6
MISSINGNESS_PROLONGED_INCREASE = 0.50
MISSINGNESS_PROLONGED_LENGTH = 5

##################################
# Defining a function for 
# simulating missingness spike
##################################
def simulate_P5_missingness_spike(df):
    # Initializing RNG for reproducibility
    rng = np.random.RandomState(RANDOM_STATE)

    # Creating time-ordered synthetic stream of data chunks
    stream = make_stream_from_dataframe(df)

    # Defining MCAR spike window
    spike_start, spike_end = N_CHUNKS // 3, N_CHUNKS // 3 + MISSINGNESS_SPIKE_LENGTH

    # Simulating MCAR (Missing Completely At Random)
    for c in range(spike_start, spike_end):
        # Identifing rows belonging to the current chunk
        mask = stream['__chunk'] == c

        for f in MCAR_FEATURES:
            # Skipping if feature not present in data
            if f not in stream.columns:
                continue

            # Indices of rows in this chunk
            idx = stream[mask].index

            # Randomly selecting a fraction of rows to make missing
            n_missing = int(len(idx) * MISSINGNESS_SPIKE_INTENSITY)
            if n_missing == 0:
                continue

            miss = rng.choice(idx, n_missing, replace=False)

            # Apply missingness
            stream.loc[miss, f] = np.nan

    # Simulating MAR (Missing At Random) based on a reference feature
    for c in range(N_CHUNKS):
        mask = stream['__chunk'] == c

        # Proceeding only if the predictor feature exists
        if 'area_mean' not in stream.columns:
            continue

        # Identify high values of 'area_mean' (top 20%)
        high_area = stream.loc[mask & (stream['area_mean'] > stream['area_mean'].quantile(0.8))].index
        if len(high_area) == 0:
            continue

        # Applying MAR missingness to multiple MAR features
        for f in MAR_FEATURES:
            if f not in stream.columns:
                continue

            n_mar = int(len(high_area) * 0.2)
            if n_mar == 0:
                continue

            miss = rng.choice(high_area, n_mar, replace=False)
            stream.loc[miss, f] = np.nan

    # Simulating Prolonged missingness pattern after spikes 
    for c in range(spike_end, spike_end + MISSINGNESS_PROLONGED_LENGTH):
        mask = stream['__chunk'] == c
        for f in MCAR_FEATURES:
            if f not in stream.columns:
                continue
            idx = stream[mask].index
            n_missing = int(len(idx) * MISSINGNESS_PROLONGED_INCREASE)
            if n_missing == 0:
                continue
            miss = rng.choice(idx, n_missing, replace=False)
            stream.loc[miss, f] = np.nan

    # Returning the modified stream with simulated missingness
    return stream

##################################
# Defining a function for 
# plotting missing fraction per chunk
# for both the simulated and baseline control
##################################
def plot_missingness(df_base, df_missing, features, scenario_name):
    # Computing the missing fraction per chunk
    def missing_rate(df):
        return df.groupby('__chunk')[features].apply(lambda x: x.isna().mean())

    # Computing missingness for baseline and simulated datasets
    miss_base = missing_rate(df_base)
    miss_sim = missing_rate(df_missing)

    # Creating a subplot per feature
    n_features = len(features)
    fig, axes = plt.subplots(n_features, 1, figsize=(12, 3 * n_features), sharex=True)
    if n_features == 1:
        axes = [axes]

    # Looping through features and plot both Baseline and Scenario
    for ax, f in zip(axes, features):
        # Plotting baseline missingness
        sns.lineplot(x=miss_base.index, y=miss_base[f], color="#4C72B0", label="Baseline", ax=ax)
        # Plotting simulated scenario missingness
        sns.lineplot(x=miss_sim.index, y=miss_sim[f], color="#DD8452", label=scenario_name, ax=ax)

        ax.set_title(f"Missingness over Time: {f} ({scenario_name} vs Baseline Control)", fontsize=11)
        ax.set_xlabel("Chunk Index")
        ax.set_ylabel("Missing Fraction")
        ax.set_ylim(-0.1, 1)
        ax.set_xticks(range(10))
        ax.grid(True, alpha=0.3)
        ax.legend(loc="best")

    plt.tight_layout()
    plt.show()

    

##################################
# Simulating post-deployment data drift scenario 5 = missingness spike
##################################
p5 = simulate_P5_missingness_spike(breast_cancer_monitoring_baseline)

##################################
# Exploring the simulated missingness spike
##################################
display(p5)

	diagnosis	radius_mean	texture_mean	perimeter_mean	area_mean	smoothness_mean	compactness_mean	concavity_mean	concave points_mean	symmetry_mean	...	perimeter_worst	area_worst	smoothness_worst	compactness_worst	concavity_worst	concave points_worst	symmetry_worst	fractal_dimension_worst	__chunk	__timestamp
0	M	17.420	25.56	114.50	948.0	0.10060	0.11460	0.168200	0.065970	0.1308	...	120.40	1021.0	0.1243	0.17930	0.280300	0.10990	0.1603	0.06818	0	0
1	M	22.270	19.67	152.80	1509.0	0.13260	NaN	0.426400	NaN	0.2556	...	206.80	2360.0	0.1701	0.69970	0.960800	0.29100	0.4055	0.09789	0	0
2	B	11.250	14.78	71.38	390.0	0.08306	0.04458	0.000974	0.002941	0.1773	...	82.08	492.7	0.1166	0.09794	0.005518	0.01667	0.2815	0.07418	0	0
3	B	12.250	22.44	78.18	466.5	0.08192	0.05200	0.017140	0.012610	0.1544	...	92.74	622.9	0.1256	0.18040	0.123000	0.06335	0.3100	0.08203	0	0
4	B	10.480	19.86	66.72	337.7	0.10700	0.05971	0.048310	0.030700	0.1737	...	73.68	402.8	0.1515	0.10260	0.118100	0.06736	0.2883	0.07748	0	0
...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...
995	B	14.030	21.25	NaN	NaN	NaN	0.06945	NaN	0.018960	0.1517	...	98.27	715.5	0.1287	0.15130	0.062310	0.07963	0.2226	0.07617	9	9
996	B	NaN	NaN	NaN	571.0	0.09916	NaN	0.053850	0.037830	0.1714	...	99.43	701.9	0.1425	0.25660	0.193500	0.12840	0.2849	0.09031	9	9
997	B	13.080	15.71	85.63	NaN	NaN	NaN	0.045680	0.031100	0.1967	...	96.09	630.5	0.1312	0.27760	0.189000	0.07283	0.3184	0.08183	9	9
998	B	8.597	18.60	NaN	NaN	0.10740	NaN	0.000000	0.000000	0.2163	...	56.65	240.1	0.1347	0.07767	0.000000	0.00000	0.3142	0.08116	9	9
999	M	19.790	NaN	130.40	1192.0	0.10150	NaN	NaN	0.114900	NaN	...	148.70	1589.0	0.1275	0.38610	0.567300	0.17320	0.3305	0.08465	9	9

1000 rows × 33 columns

##################################
# Evaluating baseline missingness
# of the simulated missingness spike scenario
# and the baseline control
##################################
plot_missingness(p1, p5, MISSINGNESS_SPIKE_FEATURES, "Missingness Spike")

##################################
# Visualizing baseline feature variability
# for the simulated missingness spike scenario
# and baseline control
##################################
plot_feature_boxplot_comparison(p1, p5, MISSINGNESS_SPIKE_FEATURES, "Missingness Spike") 

##################################
# Inspecting class distribution
# for the simulated missingness spike scenario
# and baseline control
##################################
for feat in MISSINGNESS_SPIKE_FEATURES:
    fig, ax = plt.subplots(1, 2, figsize=(14, 3), sharey=True)
    combined_min = min(p1[feat].min(), p5[feat].min()) 
    combined_max = max(p1[feat].max(), p5[feat].max()) 
    y_margin = 0.05 * (combined_max - combined_min)
    y_min, y_max = combined_min - y_margin, combined_max + y_margin
    sns.boxplot(x="diagnosis", y=feat, data=p1, ax=ax[0], order=['M', 'B'])
    ax[0].set_title(f"{feat} by Label - Baseline Control")
    ax[0].set_ylim(y_min, y_max)
    sns.boxplot(x="diagnosis", y=feat, data=p5, ax=ax[1], order=['M', 'B'])
    ax[1].set_title(f"{feat} by Label - Missingness Spike")
    ax[1].set_ylim(y_min, y_max)
    plt.show() 
    

##################################
# Detecting univariate drift for missingness spike
##################################
univariate_drift_analysis_p5 = detect_univariate_drift(p1, p5, FEATURE_COLUMNS, "Missingness Spike")

Univariate drift visualization generated for Missingness Spike
       chunk                                                                  \
       chunk                                                                   
         key chunk_index start_index end_index start_date end_date    period   
0     [0:99]           0           0        99       None     None  analysis   
1  [100:199]           1         100       199       None     None  analysis   
2  [200:299]           2         200       299       None     None  analysis   
3  [300:399]           3         300       399       None     None  analysis   
4  [400:499]           4         400       499       None     None  analysis   
5  [500:599]           5         500       599       None     None  analysis   
6  [600:699]           6         600       699       None     None  analysis   
7  [700:799]           7         700       799       None     None  analysis   
8  [800:899]           8         800       899       None     None  analysis   
9  [900:999]           9         900       999       None     None  analysis   

           area_mean                                  ...       texture_mean  \
  kolmogorov_smirnov                                  ... kolmogorov_smirnov   
               value upper_threshold lower_threshold  ...    lower_threshold   
0              0.040        0.150643            None  ...               None   
1              0.089        0.150643            None  ...               None   
2              0.068        0.150643            None  ...               None   
3              0.130        0.150643            None  ...               None   
4              0.173        0.150643            None  ...               None   
5              0.121        0.150643            None  ...               None   
6              0.218        0.150643            None  ...               None   
7              0.175        0.150643            None  ...               None   
8              0.115        0.150643            None  ...               None   
9              0.099        0.150643            None  ...               None   

                 texture_se                                         \
         kolmogorov_smirnov                                          
   alert              value upper_threshold lower_threshold  alert   
0  False              0.066         0.09887            None  False   
1  False              0.061         0.09887            None  False   
2  False              0.085         0.09887            None  False   
3   True              0.054         0.09887            None  False   
4   True              0.061         0.09887            None  False   
5  False              0.036         0.09887            None  False   
6   True              0.068         0.09887            None  False   
7  False              0.060         0.09887            None  False   
8   True              0.073         0.09887            None  False   
9  False              0.064         0.09887            None  False   

       texture_worst                                         
  kolmogorov_smirnov                                         
               value upper_threshold lower_threshold  alert  
0              0.097        0.140661            None  False  
1              0.074        0.140661            None  False  
2              0.053        0.140661            None  False  
3              0.076        0.140661            None  False  
4              0.064        0.140661            None  False  
5              0.068        0.140661            None  False  
6              0.125        0.140661            None  False  
7              0.060        0.140661            None  False  
8              0.090        0.140661            None  False  
9              0.091        0.140661            None  False  

[10 rows x 127 columns]

##################################
# Visualizing univariate drift for missingness spike
##################################
univariate_drift_analysis_visualization_p5 = plot_univariate_drift_summary(univariate_drift_analysis_p5, FEATURE_COLUMNS, "Missingness Spike")

Univariate Drift Summary Table:

	feature	chunk_drift_count
0	radius_mean	6
1	texture_mean	4
2	perimeter_mean	5
3	area_mean	3
4	smoothness_mean	4
5	compactness_mean	3
6	concavity_mean	6
7	concave points_mean	0
8	symmetry_mean	0
9	fractal_dimension_mean	0
10	radius_se	0
11	texture_se	0
12	perimeter_se	0
13	area_se	0
14	smoothness_se	0
15	compactness_se	0
16	concavity_se	0
17	concave points_se	0
18	symmetry_se	0
19	fractal_dimension_se	0
20	radius_worst	0
21	texture_worst	0
22	perimeter_worst	0
23	area_worst	0
24	smoothness_worst	0
25	compactness_worst	0
26	concavity_worst	0
27	concave points_worst	0
28	symmetry_worst	0
29	fractal_dimension_worst	0

##################################
# Estimating CBPE performance for missingness spike
##################################
chunk_cbpe_performance_analysis_p5 = estimate_chunk_cbpe_performance(p1, p5, boosted_cb_optimal, FEATURE_COLUMNS)

Chunk CBPE Performance Summary Table:

	chunk							roc_auc
	key	chunk_index	start_index	end_index	start_date	end_date	period	value	sampling_error	realized	upper_confidence_boundary	lower_confidence_boundary	upper_threshold	lower_threshold	alert
0	[0:99]	0	0	99	None	None	reference	0.994438	0.00367	0.9924	1.000000	0.983427	1	0.976509	False
1	[100:199]	1	100	199	None	None	reference	0.997225	0.00367	0.9972	1.000000	0.986213	1	0.976509	False
2	[200:299]	2	200	299	None	None	reference	0.997486	0.00367	1.0000	1.000000	0.986475	1	0.976509	False
3	[300:399]	3	300	399	None	None	reference	0.995054	0.00367	0.9924	1.000000	0.984043	1	0.976509	False
4	[400:499]	4	400	499	None	None	reference	0.996828	0.00367	0.9928	1.000000	0.985817	1	0.976509	False
5	[500:599]	5	500	599	None	None	reference	0.995083	0.00367	0.9936	1.000000	0.984072	1	0.976509	False
6	[600:699]	6	600	699	None	None	reference	0.996123	0.00367	0.9960	1.000000	0.985111	1	0.976509	False
7	[700:799]	7	700	799	None	None	reference	0.995848	0.00367	0.9960	1.000000	0.984836	1	0.976509	False
8	[800:899]	8	800	899	None	None	reference	0.991864	0.00367	0.9780	1.000000	0.980853	1	0.976509	False
9	[900:999]	9	900	999	None	None	reference	0.994634	0.00367	0.9964	1.000000	0.983623	1	0.976509	False
10	[0:99]	0	0	99	None	None	analysis	0.994438	0.00367	NaN	1.000000	0.983427	1	0.976509	False
11	[100:199]	1	100	199	None	None	analysis	0.997225	0.00367	NaN	1.000000	0.986213	1	0.976509	False
12	[200:299]	2	200	299	None	None	analysis	0.997486	0.00367	NaN	1.000000	0.986475	1	0.976509	False
13	[300:399]	3	300	399	None	None	analysis	0.991720	0.00367	NaN	1.000000	0.980708	1	0.976509	False
14	[400:499]	4	400	499	None	None	analysis	0.995417	0.00367	NaN	1.000000	0.984406	1	0.976509	False
15	[500:599]	5	500	599	None	None	analysis	0.993748	0.00367	NaN	1.000000	0.982737	1	0.976509	False
16	[600:699]	6	600	699	None	None	analysis	0.988016	0.00367	NaN	0.999027	0.977004	1	0.976509	False
17	[700:799]	7	700	799	None	None	analysis	0.994608	0.00367	NaN	1.000000	0.983596	1	0.976509	False
18	[800:899]	8	800	899	None	None	analysis	0.988792	0.00367	NaN	0.999803	0.977780	1	0.976509	False
19	[900:999]	9	900	999	None	None	analysis	0.992945	0.00367	NaN	1.000000	0.981934	1	0.976509	False

##################################
# Visualizing CBPE performance for missingness spike
##################################
chunk_cbpe_performance_analysis_visualization_p5 = plot_chunk_cbpe_performance(chunk_cbpe_performance_analysis_p5, baseline_name="Baseline Control", scenario_name="Missingness Spike")

Chunk CBPE Performance Summary Table:

	chunk_chunk_index	chunk_period	cbpe_roc_auc_alert_count
0	0	analysis	0
1	0	reference	0
2	1	analysis	0
3	1	reference	0
4	2	analysis	0
5	2	reference	0
6	3	analysis	0
7	3	reference	0
8	4	analysis	0
9	4	reference	0
10	5	analysis	0
11	5	reference	0
12	6	analysis	0
13	6	reference	0
14	7	analysis	0
15	7	reference	0
16	8	analysis	0
17	8	reference	0
18	9	analysis	0
19	9	reference	0

1.9.6 Simulated Seasonal Pattern

##################################
# Defining the seasonal pattern-specific parameters
# for the post-model deployment scenario simulation
##################################
SEASONAL_PATTERN_FEATURES = ['radius_mean','texture_mean','perimeter_mean','area_mean','smoothness_mean',
'compactness_mean','concavity_mean','concave points_mean','symmetry_mean','fractal_dimension_mean']
SEASONAL_AMPLITUDE_SIGMAS = 0.5
SEASONAL_PERIOD = 10

##################################
# Defining a function for 
# simulating seasonal pattern
##################################
def simulate_P6_seasonal(df):
    # Creating a time-ordered synthetic stream of data chunks
    stream = make_stream_from_dataframe(df)
    # Computing standard deviations of seasonal features (used to scale amplitude)
    stds = df[SEASONAL_PATTERN_FEATURES].std()
    # Looping through each chunk (simulated time window)
    for c in range(N_CHUNKS):
        # Identifying the subset of rows belonging to the current chunk
        mask = stream['__chunk']==c
        # Applying sinusoidal seasonal pattern to each selected feature
        for f in SEASONAL_PATTERN_FEATURES:
            # Defining the amplitude of the seasonal signal (A = SEASONAL_AMPLITUDE_SIGMAS × feature std)
            amp = SEASONAL_AMPLITUDE_SIGMAS * stds[f]
            # Applying sinusoidal variation based on the chunk index (acting as a proxy for time)
            stream.loc[mask, f] += amp * np.sin(2 * np.pi * c / SEASONAL_PERIOD)
    # Returning the modified data stream with simulated seasonality
    return stream

##################################
# Simulating post-deployment data drift scenario 6 = seasonal pattern
##################################
p6 = simulate_P6_seasonal(breast_cancer_monitoring_baseline)

##################################
# Exploring the simulated seasonal pattern
##################################
display(p6)

	diagnosis	radius_mean	texture_mean	perimeter_mean	area_mean	smoothness_mean	compactness_mean	concavity_mean	concave points_mean	symmetry_mean	...	perimeter_worst	area_worst	smoothness_worst	compactness_worst	concavity_worst	concave points_worst	symmetry_worst	fractal_dimension_worst	__chunk	__timestamp
0	M	17.420000	25.560000	114.500000	948.000000	0.100600	0.114600	0.168200	0.065970	0.130800	...	120.40	1021.0	0.1243	0.17930	0.280300	0.10990	0.1603	0.06818	0	0
1	M	22.270000	19.670000	152.800000	1509.000000	0.132600	0.276800	0.426400	0.182300	0.255600	...	206.80	2360.0	0.1701	0.69970	0.960800	0.29100	0.4055	0.09789	0	0
2	B	11.250000	14.780000	71.380000	390.000000	0.083060	0.044580	0.000974	0.002941	0.177300	...	82.08	492.7	0.1166	0.09794	0.005518	0.01667	0.2815	0.07418	0	0
3	B	12.250000	22.440000	78.180000	466.500000	0.081920	0.052000	0.017140	0.012610	0.154400	...	92.74	622.9	0.1256	0.18040	0.123000	0.06335	0.3100	0.08203	0	0
4	B	10.480000	19.860000	66.720000	337.700000	0.107000	0.059710	0.048310	0.030700	0.173700	...	73.68	402.8	0.1515	0.10260	0.118100	0.06736	0.2883	0.07748	0	0
...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...
995	B	13.001295	20.070771	82.714167	501.412888	0.086328	0.052944	-0.009284	0.007443	0.143055	...	98.27	715.5	0.1287	0.15130	0.062310	0.07963	0.2226	0.07617	9	9
996	B	12.681295	17.500771	81.654167	469.012888	0.094788	0.090494	0.029946	0.026313	0.162755	...	99.43	701.9	0.1425	0.25660	0.193500	0.12840	0.2849	0.09031	9	9
997	B	12.051295	14.530771	78.554167	418.012888	0.103128	0.110494	0.021776	0.019583	0.188055	...	96.09	630.5	0.1312	0.27760	0.189000	0.07283	0.3184	0.08183	9	9
998	B	7.568295	17.420771	47.014167	119.212888	0.103028	0.041964	-0.023904	-0.011517	0.207655	...	56.65	240.1	0.1347	0.07767	0.000000	0.00000	0.3142	0.08116	9	9
999	M	18.761295	23.940771	123.324167	1090.012888	0.097128	0.142394	0.230596	0.103383	0.211555	...	148.70	1589.0	0.1275	0.38610	0.567300	0.17320	0.3305	0.08465	9	9

1000 rows × 33 columns

##################################
# Visualizing baseline feature variability
# of the simulated seasonal pattern scenario
# and the baseline control
##################################
plot_feature_mean_line(p1, p6, SEASONAL_PATTERN_FEATURES, "Seasonal Pattern")

##################################
# Visualizing baseline feature variability
# for the simulated seasonal pattern scenario
# and baseline control
##################################
plot_feature_boxplot_comparison(p1, p6, SEASONAL_PATTERN_FEATURES, "Seasonal Pattern")

##################################
# Inspecting class distribution
# for the simulated seasonal pattern scenario
# and baseline control
##################################
for feat in SEASONAL_PATTERN_FEATURES:
    fig, ax = plt.subplots(1, 2, figsize=(14, 3), sharey=True)
    combined_min = min(p1[feat].min(), p6[feat].min()) 
    combined_max = max(p1[feat].max(), p6[feat].max()) 
    y_margin = 0.05 * (combined_max - combined_min)
    y_min, y_max = combined_min - y_margin, combined_max + y_margin
    sns.boxplot(x="diagnosis", y=feat, data=p1, ax=ax[0], order=['M', 'B'])
    ax[0].set_title(f"{feat} by Label - Baseline Control")
    ax[0].set_ylim(y_min, y_max)
    sns.boxplot(x="diagnosis", y=feat, data=p6, ax=ax[1], order=['M', 'B'])
    ax[1].set_title(f"{feat} by Label - Seasonal Pattern")
    ax[1].set_ylim(y_min, y_max)
    plt.show()
    

##################################
# Detecting univariate drift for seasonal pattern
##################################
univariate_drift_analysis_p6 = detect_univariate_drift(p1, p6, FEATURE_COLUMNS, "Seasonal Pattern")

Univariate drift visualization generated for Seasonal Pattern
       chunk                                                                  \
       chunk                                                                   
         key chunk_index start_index end_index start_date end_date    period   
0     [0:99]           0           0        99       None     None  analysis   
1  [100:199]           1         100       199       None     None  analysis   
2  [200:299]           2         200       299       None     None  analysis   
3  [300:399]           3         300       399       None     None  analysis   
4  [400:499]           4         400       499       None     None  analysis   
5  [500:599]           5         500       599       None     None  analysis   
6  [600:699]           6         600       699       None     None  analysis   
7  [700:799]           7         700       799       None     None  analysis   
8  [800:899]           8         800       899       None     None  analysis   
9  [900:999]           9         900       999       None     None  analysis   

           area_mean                                  ...       texture_mean  \
  kolmogorov_smirnov                                  ... kolmogorov_smirnov   
               value upper_threshold lower_threshold  ...    lower_threshold   
0              0.040        0.150643            None  ...               None   
1              0.234        0.150643            None  ...               None   
2              0.314        0.150643            None  ...               None   
3              0.338        0.150643            None  ...               None   
4              0.243        0.150643            None  ...               None   
5              0.055        0.150643            None  ...               None   
6              0.252        0.150643            None  ...               None   
7              0.348        0.150643            None  ...               None   
8              0.291        0.150643            None  ...               None   
9              0.162        0.150643            None  ...               None   

                 texture_se                                         \
         kolmogorov_smirnov                                          
   alert              value upper_threshold lower_threshold  alert   
0  False              0.066         0.09887            None  False   
1   True              0.061         0.09887            None  False   
2   True              0.085         0.09887            None  False   
3   True              0.054         0.09887            None  False   
4   True              0.061         0.09887            None  False   
5  False              0.036         0.09887            None  False   
6   True              0.068         0.09887            None  False   
7   True              0.060         0.09887            None  False   
8   True              0.073         0.09887            None  False   
9   True              0.064         0.09887            None  False   

       texture_worst                                         
  kolmogorov_smirnov                                         
               value upper_threshold lower_threshold  alert  
0              0.097        0.140661            None  False  
1              0.074        0.140661            None  False  
2              0.053        0.140661            None  False  
3              0.076        0.140661            None  False  
4              0.064        0.140661            None  False  
5              0.068        0.140661            None  False  
6              0.125        0.140661            None  False  
7              0.060        0.140661            None  False  
8              0.090        0.140661            None  False  
9              0.091        0.140661            None  False  

[10 rows x 127 columns]

##################################
# Visualizing univariate drift for seasonal pattern
##################################
univariate_drift_analysis_visualization_p6 = plot_univariate_drift_summary(univariate_drift_analysis_p6, FEATURE_COLUMNS, "Seasonal Pattern")

Univariate Drift Summary Table:

	feature	chunk_drift_count
0	radius_mean	7
1	texture_mean	8
2	perimeter_mean	8
3	area_mean	8
4	smoothness_mean	7
5	compactness_mean	8
6	concavity_mean	8
7	concave points_mean	8
8	symmetry_mean	7
9	fractal_dimension_mean	8
10	radius_se	0
11	texture_se	0
12	perimeter_se	0
13	area_se	0
14	smoothness_se	0
15	compactness_se	0
16	concavity_se	0
17	concave points_se	0
18	symmetry_se	0
19	fractal_dimension_se	0
20	radius_worst	0
21	texture_worst	0
22	perimeter_worst	0
23	area_worst	0
24	smoothness_worst	0
25	compactness_worst	0
26	concavity_worst	0
27	concave points_worst	0
28	symmetry_worst	0
29	fractal_dimension_worst	0

##################################
# Estimating CBPE performance for seasonal pattern
##################################
chunk_cbpe_performance_analysis_p6 = estimate_chunk_cbpe_performance(p1, p6, boosted_cb_optimal, FEATURE_COLUMNS)

Chunk CBPE Performance Summary Table:

	chunk							roc_auc
	key	chunk_index	start_index	end_index	start_date	end_date	period	value	sampling_error	realized	upper_confidence_boundary	lower_confidence_boundary	upper_threshold	lower_threshold	alert
0	[0:99]	0	0	99	None	None	reference	0.994438	0.00367	0.9924	1.000000	0.983427	1	0.976509	False
1	[100:199]	1	100	199	None	None	reference	0.997225	0.00367	0.9972	1.000000	0.986213	1	0.976509	False
2	[200:299]	2	200	299	None	None	reference	0.997486	0.00367	1.0000	1.000000	0.986475	1	0.976509	False
3	[300:399]	3	300	399	None	None	reference	0.995054	0.00367	0.9924	1.000000	0.984043	1	0.976509	False
4	[400:499]	4	400	499	None	None	reference	0.996828	0.00367	0.9928	1.000000	0.985817	1	0.976509	False
5	[500:599]	5	500	599	None	None	reference	0.995083	0.00367	0.9936	1.000000	0.984072	1	0.976509	False
6	[600:699]	6	600	699	None	None	reference	0.996123	0.00367	0.9960	1.000000	0.985111	1	0.976509	False
7	[700:799]	7	700	799	None	None	reference	0.995848	0.00367	0.9960	1.000000	0.984836	1	0.976509	False
8	[800:899]	8	800	899	None	None	reference	0.991864	0.00367	0.9780	1.000000	0.980853	1	0.976509	False
9	[900:999]	9	900	999	None	None	reference	0.994634	0.00367	0.9964	1.000000	0.983623	1	0.976509	False
10	[0:99]	0	0	99	None	None	analysis	0.994438	0.00367	NaN	1.000000	0.983427	1	0.976509	False
11	[100:199]	1	100	199	None	None	analysis	0.997635	0.00367	NaN	1.000000	0.986624	1	0.976509	False
12	[200:299]	2	200	299	None	None	analysis	0.996538	0.00367	NaN	1.000000	0.985527	1	0.976509	False
13	[300:399]	3	300	399	None	None	analysis	0.987125	0.00367	NaN	0.998136	0.976113	1	0.976509	False
14	[400:499]	4	400	499	None	None	analysis	0.996764	0.00367	NaN	1.000000	0.985753	1	0.976509	False
15	[500:599]	5	500	599	None	None	analysis	0.995083	0.00367	NaN	1.000000	0.984072	1	0.976509	False
16	[600:699]	6	600	699	None	None	analysis	0.994447	0.00367	NaN	1.000000	0.983435	1	0.976509	False
17	[700:799]	7	700	799	None	None	analysis	0.995009	0.00367	NaN	1.000000	0.983997	1	0.976509	False
18	[800:899]	8	800	899	None	None	analysis	0.991854	0.00367	NaN	1.000000	0.980842	1	0.976509	False
19	[900:999]	9	900	999	None	None	analysis	0.993473	0.00367	NaN	1.000000	0.982462	1	0.976509	False

##################################
# Visualizing CBPE performance for seasonal pattern
##################################
chunk_cbpe_performance_analysis_visualization_p6 = plot_chunk_cbpe_performance(chunk_cbpe_performance_analysis_p6, baseline_name="Baseline Control", scenario_name="Seasonal Pattern")

Chunk CBPE Performance Summary Table:

	chunk_chunk_index	chunk_period	cbpe_roc_auc_alert_count
0	0	analysis	0
1	0	reference	0
2	1	analysis	0
3	1	reference	0
4	2	analysis	0
5	2	reference	0
6	3	analysis	0
7	3	reference	0
8	4	analysis	0
9	4	reference	0
10	5	analysis	0
11	5	reference	0
12	6	analysis	0
13	6	reference	0
14	7	analysis	0
15	7	reference	0
16	8	analysis	0
17	8	reference	0
18	9	analysis	0
19	9	reference	0

1.10. Consolidated Findings

2. Summary

3. References

• [Book] Reliable Machine Learning by Cathy Chen, Niall Richard Murphy, Kranti Parisa, D. Sculley and Todd Underwood
• [Book] Designing Machine Learning Systems by Chip Huyen
• [Book] Machine Learning Design Patterns by Valliappa Lakshmanan, Sara Robinson and Michael Munn
• [Book] Machine Learning Engineering by Andriy Burkov
• [Book] Engineering MLOps by Emmanuel Raj
• [Book] Introducing MLOps by Mark Treveil, Nicolas Omont, Clément Stenac, Kenji Lefevre, Du Phan, Joachim Zentici, Adrien Lavoillotte, Makoto Miyazaki and Lynn Heidmann
• [Book] Practical MLOps by Noah Gift and Alfredo Deza
• [Book] Data Science on AWS by Chris Fregly and Antje Barth
• [Book] Ensemble Methods for Machine Learning by Gautam Kunapuli
• [Book] Applied Predictive Modeling by Max Kuhn and Kjell Johnson
• [Book] An Introduction to Statistical Learning by Gareth James, Daniela Witten, Trevor Hastie and Rob Tibshirani
• [Book] Ensemble Methods: Foundations and Algorithms by Zhi-Hua Zhou
• [Book] Effective XGBoost: Optimizing, Tuning, Understanding, and Deploying Classification Models (Treading on Python) by Matt Harrison, Edward Krueger, Alex Rook, Ronald Legere and Bojan Tunguz
• [Python Library API] nannyML by NannyML Team
• [Python Library API] NumPy by NumPy Team
• [Python Library API] pandas by Pandas Team
• [Python Library API] seaborn by Seaborn Team
• [Python Library API] matplotlib.pyplot by MatPlotLib Team
• [Python Library API] itertools by Python Team
• [Python Library API] sklearn.experimental by Scikit-Learn Team
• [Python Library API] sklearn.preprocessing by Scikit-Learn Team
• [Python Library API] scipy by SciPy Team
• [Python Library API] sklearn.tree by Scikit-Learn Team
• [Python Library API] sklearn.ensemble by Scikit-Learn Team
• [Python Library API] sklearn.metrics by Scikit-Learn Team
• [Python Library API] xgboost by XGBoost Team
• [Python Library API] lightgbm by LightGBM Team
• [Python Library API] catboost by CatBoost Team
• [Python Library API] StatsModels by StatsModels Team
• [Python Library API] SciPy by SciPy Team
• [Article] Comprehensive Comparison of ML Model Monitoring Tools: Evidently AI, Alibi Detect, NannyML, WhyLabs, and Fiddler AI by Tanish Kandivlikar (Medium)
• [Article] Monitoring AI in Production: Introduction to NannyML by Adnan Karol (Medium)
• [Article] Data Drift Explainability: Interpretable Shift Detection with NannyML by Marco Cerliani (Towards Data Science)
• [Article] An End-to-End ML Model Monitoring Workflow with NannyML in Python by Bex Tuychiyev (DataCamp)
• [Article] Detecting Concept Drift: Impact on Machine Learning Performance by Michal Oleszak (NannyML.Com)
• [Article] Estimating Model Performance Without Labels by Jakub Białek (NannyML.Com)
• [Article] Monitoring Workflow for Machine Learning Systems by Santiago Víquez (NannyML.Com)
• [Article] Don’t Let Yourself Be Fooled by Data Drift by Santiago Víquez (NannyML.Com)
• [Article] Understanding Data Drift: Impact on Machine Learning Model Performance by Jakub Białek (NannyML.Com)
• [Article] NannyML’s Guide to Data Quality and Covariate Shift by Magdalena Kowalczuk (NannyML.Com)
• [Article] From Reactive to Proactive: Shift your ML Monitoring Approach by Qiamo (Luca) Zheng (NannyML.Com)
• [Article] How to Detect Under-Performing Segments in ML Models by Kavita Rana (NannyML.Com)
• [Article] Building Custom Metrics for Predictive Maintenance by Kavita Rana(NannyML.Com)
• [Article] 3 Custom Metrics for Your Forecasting Models by Kavita Rana (NannyML.Com)
• [Article] There's Data Drift, But Does It Matter? by Santiago Víquez (NannyML.Com)
• [Article] Monitoring Custom Metrics without Ground Truth by Kavita Rana (NannyML.Com)
• [Article] Which Multivariate Drift Detection Method Is Right for You: Comparing DRE and DC by Miles Weberman (NannyML.Com)
• [Article] Prevent Failure of Product Defect Detection Models: A Post-Deployment Guide by Kavita Rana (NannyML.Com)
• [Article] Common Pitfalls in Monitoring Default Prediction Models and How to Fix Them by Miles Weberman (NannyML.Com)
• [Article] Why Relying on Training Data for ML Monitoring Can Trick You by Kavita Rana (NannyML.Com)
• [Article] Estimating Model Performance Without Labels by Jakub Białek (NannyML.Com)
• [Article] Using Concept Drift as a Model Retraining Trigger by Taliya Weinstein (NannyML.Com)
• [Article] Retraining is Not All You Need by Miles Weberman (NannyML.Com)
• [Article] A Comprehensive Guide to Univariate Drift Detection Methods by Kavita Rana (NannyML.Com)
• [Article] Stress-free Monitoring of Predictive Maintenance Models by Kavita Rana (NannyML.Com)
• [Article] Effective ML Monitoring: A Hands-on Example by Miles Weberman (NannyML.Com)
• [Article] Don’t Drift Away with Your Data: Monitoring Data Drift from Setup to Cloud by Taliya Weinstein (NannyML.Com)
• [Article] Comparing Multivariate Drift Detection Algorithms on Real-World Data by Kavita Rana (NannyML.Com)
• [Article] Detect Data Drift Using Domain Classifier in Python by Miles Weberman (NannyML.Com)
• [Article] Guide: How to evaluate if NannyML is the right monitoring tool for you by Santiago Víquez (NannyML.Com)
• [Article] How To Monitor ML models with NannyML SageMaker Algorithms by Wiljan Cools (NannyML.Com)
• [Article] Tutorial: Monitoring Missing and Unseen values with NannyML by Santiago Víquez (NannyML.Com)
• [Article] Monitoring Machine Learning Models: A Fundamental Practice for Data Scientists and Machine Learning Engineers by Saurav Pawar (Medium)
• [Article] Failure Is Not an Option: How to Prevent Your ML Model From Degradation by Maciej Balawejder (Medium)
• [Article] Managing Data Drift and Data Distribution Shifts in the MLOps Lifecycle for Machine Learning Models by Abhishek Reddy (Medium)
• [Article] “You Can’t Predict the Errors of Your Model”… Or Can You? by Samuele Mazzanti (Medium)
• [Article] Understanding Concept Drift: A Simple Guide by Vitor Cerqueira (Medium)
• [Article] Detecting Covariate Shift: A Guide to the Multivariate Approach by Michał Oleszak (Medium)
• [Article] Data Drift vs. Concept Drift: Differences and How to Detect and Address Them by DataHeroes Team (DataHeroes.AI)
• [Article] An Introduction to Machine Learning Engineering for Production /MLOps — Concept and Data Drifts by Praatibh Surana (Medium)
• [Article] Concept Drift and Model Decay in Machine Learning by Ashok Chilakapati (Medium)
• [Article] Data Drift: Types of Data Drift by Numal Jayawardena (Medium)
• [Article] Monitoring Machine Learning models by Jacques Verre (Medium)
• [Article] Data drift: It Can Come At You From Anywhere by Tirthajyoti Sarkar (Medium)
• [Article] Drift in Machine Learning by Piotr (Peter) Mardziel (Medium)
• [Article] Understanding Dataset Shift by Matthew Stewart (Medium)
• [Article] Calculating Data Drift in Machine Learning using Python by Vatsal (Medium)
• [Article] 91% of ML Models Degrade in Time by Santiago Víquez (Medium)
• [Article] Model Drift in Machine Learning by Kurtis Pykes (Medium)
• [Article] Production Machine Learning Monitoring: Outliers, Drift, Explainers & Statistical Performance by Alejandro Saucedo (Medium)
• [Article] How to Detect Model Drift in MLOps Monitoring by Amit Paka (Medium)
• [Article] “My data drifted. What’s next?” How to handle ML model drift in production. by Elena Samuylova (Medium)
• [Article] Machine Learning Model Drift by Sophia Yang (Medium)
• [Article] Estimating the Performance of an ML Model in the Absence of Ground Truth by Eryk Lewinson (Medium)
• [Article] Ensemble: Boosting, Bagging, and Stacking Machine Learning by Jason Brownlee (MachineLearningMastery.Com)
• [Article] Stacking Machine Learning: Everything You Need to Know by Ada Parker (MachineLearningPro.Org)
• [Article] Ensemble Learning: Bagging, Boosting and Stacking by Edouard Duchesnay, Tommy Lofstedt and Feki Younes (Duchesnay.GitHub.IO)
• [Article] Stack Machine Learning Models: Get Better Results by Casper Hansen (Developer.IBM.Com)
• [Article] GradientBoosting vs AdaBoost vs XGBoost vs CatBoost vs LightGBM by Geeks for Geeks Team (GeeksForGeeks.Org)
• [Article] A Gentle Introduction to the Gradient Boosting Algorithm for Machine Learning by Jason Brownlee (MachineLearningMastery.Com)
• [Article] The Ultimate Guide to AdaBoost Algorithm | What is AdaBoost Algorithm? by Ashish Kumar (MyGreatLearning.Com)
• [Article] A Gentle Introduction to Ensemble Learning Algorithms by Jason Brownlee (MachineLearningMastery.Com)
• [Article] Ensemble Methods: Elegant Techniques to Produce Improved Machine Learning Results by Necati Demir (Toptal.Com)
• [Article] The Essential Guide to Ensemble Learning by Rohit Kundu (V7Labs.Com)
• [Article] Develop an Intuition for How Ensemble Learning Works by by Jason Brownlee (Machine Learning Mastery)
• [Article] Mastering Ensemble Techniques in Machine Learning: Bagging, Boosting, Bayes Optimal Classifier, and Stacking by Rahul Jain (Medium)
• [Article] Ensemble Learning: Bagging, Boosting, Stacking by Ayşe Kübra Kuyucu (Medium)
• [Article] Ensemble: Boosting, Bagging, and Stacking Machine Learning by Aleyna Şenozan (Medium)
• [Article] Boosting, Stacking, and Bagging for Ensemble Models for Time Series Analysis with Python by Kyle Jones (Medium)
• [Article] Different types of Ensemble Techniques — Bagging, Boosting, Stacking, Voting, Blending by Abhishek Jain (Medium)
• [Article] Mastering Ensemble Techniques in Machine Learning: Bagging, Boosting, Bayes Optimal Classifier, and Stacking by Rahul Jain (Medium)
• [Article] Understanding Ensemble Methods: Bagging, Boosting, and Stacking by Divya bhagat (Medium)
• [Video Tutorial] Concept Drift Detection with NannyML | Webinar by NannyML (YouTube)
• [Video Tutorial] Fooled by Data Drift: How to Monitor ML Without False Positives by NannyML (YouTube)
• [Video Tutorial] Monitoring Custom Metrics Without Access to Targets by NannyML (YouTube)
• [Video Tutorial] Analyzing Your Model's Performance in Production by NannyML (YouTube)
• [Video Tutorial] How to Monitor Predictive Maintenance Models | Webinar Replay by NannyML (YouTube)
• [Video Tutorial] Machine Learning Monitoring Workflow [Webinar] by NannyML (YouTube)
• [Video Tutorial] Monitoring Machine Learning Models on AWS | Webinar by NannyML (YouTube)
• [Video Tutorial] Root Cause Analysis for ML Model Failure by NannyML (YouTube)
• [Video Tutorial] Quantifying the Impact of Data Drift on Machine Learning Model Performance | Webinar by NannyML (YouTube)
• [Video Tutorial] How to Detect Drift and Resolve Issues in Your Machine Learning Models? by NannyML (YouTube)
• [Video Tutorial] Notebooks to Containers: Setting up Continuous (ML) Model Monitoring in Production by NannyML (YouTube)
• [Video Tutorial] Performance Estimation using NannyML | Tutorial in Jupyter Notebook by NannyML (YouTube)
• [Video Tutorial] What Is NannyML? Introducing Our Open Source Python Library by NannyML (YouTube)
• [Video Tutorial] How to Automatically Retrain Your Models with Concept Drift Detection? by NannyML (YouTube)
• [Video Tutorial] How to Use NannyML? Two Modes of Running Our Library by NannyML (YouTube)
• [Video Tutorial] How to Integrate NannyML in Production? | Tutorial by NannyML (YouTube)
• [Video Tutorial] Bringing Your Machine Learning Model to Production | Overview by NannyML (YouTube)
• [Video Tutorial] Notebooks to Containers: Setting Up Continuous (ML) Model Monitoring in Production by NannyML (YouTube)
• [Video Tutorial] ML Performance without Labels: Comparing Performance Estimation Methods (Webinar Replay) by NannyML (YouTube)
• [Course] DataCamp Python Data Analyst Certificate by DataCamp Team (DataCamp)
• [Course] DataCamp Python Associate Data Scientist Certificate by DataCamp Team (DataCamp)
• [Course] DataCamp Python Data Scientist Certificate by DataCamp Team (DataCamp)
• [Course] DataCamp Machine Learning Engineer Certificate by DataCamp Team (DataCamp)
• [Course] DataCamp Machine Learning Scientist Certificate by DataCamp Team (DataCamp)
• [Course] IBM Data Analyst Professional Certificate by IBM Team (Coursera)
• [Course] IBM Data Science Professional Certificate by IBM Team (Coursera)
• [Course] IBM Machine Learning Professional Certificate by IBM Team (Coursera)